Forecasting Urban Population Growth in Somalia: Using ARIMA, TBATS, NNAR, and Hybrid Models

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Accurate forecasting of urban population growth is essential for effective urban planning and resource management. This study employs ARIMA, TBATS, NNAR, and hybrid models to forecast urban population growth in Somalia, utilizing historical data from 1961 to 2022 sourced from the World Bank. The analysis evaluates the performance of single models and hybrid combinations (ARIMA-TBATS, ARIMA-NNAR, ARIMA-TBATS-NNAR) based on metrics including Theil’s U statistic, MAPE, SMAPE, and RMSE. Results indicate that the TBATS model best fits among the single time-series models, while the ARIMA-TBATS-NNAR hybrid model outperforms the others in forecasting urban population growth. The validated models effectively predict an increase in urban residents in Somalia from 2022 to 2033. This study underscores the importance of leveraging advanced statistical modeling, particularly hybrid approaches, to inform evidence-based strategies and optimize resource allocation for sustainable urban development in Somalia, contributing to achieving Sustainable Development Goals (SDGs) 11 and 7 and instilling hope for a more sustainable future. Urban Population Growth Forecasting Time Series Analysis ARIMA TBATS NNAR Hybrid Models Somalia Urban Planning Sustainable Development Goals Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Introduction Urbanization has led to over half of the world's population residing in densely populated urban areas, drastically altering lifestyles, work habits, transportation, and social networks. This significant shift, a recent development in human history, is explored through historical contexts, current patterns, and future projections.[ 1 ]The study predicts that global urban areas will continue to expand significantly, with forecasts indicating an increase from approximately 1.5 million square kilometers in 2018 to over 3 million square kilometers by 2100 under various Shared Socio-economic Pathways (SSPs). This growth is driven by population increase and economic development, with urban areas in regions like Asia, particularly China, expected to see the most substantial growth. [ 2 ]A study conducted in China and other Asian countries shows that land is projected to expand significantly. Estimates indicate that by 2100, urban areas will grow the largest under the SSP5 scenario, surpassing other scenarios. Urban population declines in regions like China may lead to a sharp decrease in urban land demand after the 2040s/2050s due to demographic changes. [ 3 ] Another study utilized the ARIMA (1, 1, 10) model to forecast urban population growth in Nigeria from 2023 to 2030, based on historical data from 1961 to 2022. The model demonstrated strong predictive accuracy, effectively capturing urbanization trends. The findings indicated a significant increase in Nigeria's urban population during the forecast period. [ 4 ]. The application of Seasonal ARIMA (SARIMA) modeling in the study of urbanization growth in Vellore, India, indicated a significant increase in built-up density from 1991 to 2019, with predictions suggesting continued growth towards outer zones by 2045. The analysis revealed that built-up density decreases with increasing distance from the city center and major roads, highlighting a trend of urban expansion in less developed areas. [ 5 ]. Another study indicates a statistical dynamics framework for urbanization that incorporates agents' strategic behaviors to predict growth rates and emergent properties of cities, validated through simulations and analysis of 382 US Metropolitan Areas over nearly five decades.[ 6 ]Urbanization growth refers to developing urban areas that harness sustainable practices to enhance communities' economic, social, and environmental well-being while maintaining their unique identities. [ 7 ] Urbanization in Somalia is rapidly increasing, with the urban population rising from about 30% in 1990 to over 50% by 2020, and projections suggest it could reach 60% by 2030. Mogadishu, the capital, has seen its population grow from approximately 1 million in 2000 to over 2.5 million in 2021. However, this urban growth presents challenges, particularly in energy supply, as only 36% of the population had access to electricity in 2019, significantly lower than in neighboring countries like Kenya and Ethiopia. [ 8 ]. A high-resolution global dataset of urban dynamics from 1870 to 2100 was created as part of the study. This dataset reveals that urban growth under the SSP5 scenario has resulted in over a 40-fold increase in urban extent since 1870, providing valuable insights into the long-term environmental impacts of urbanization. The dataset includes detailed information on population growth, land use changes, and energy consumption, among other factors, and is a key resource for understanding the dynamics of urbanization in Somalia. The primary aim of this study is to establish a predictive model for urban population growth in Somalia by employing a combination of advanced statistical methods, including the Autoregressive Integrated Moving Average (ARIMA), TBATS, NNAR, and hybrid models. This comprehensive approach, backed by thorough research, enhances the accuracy of forecasts, providing critical insights for policymakers to effectively navigate the challenges posed by rapid urbanization, particularly regarding infrastructure and energy supply. By integrating multiple modeling techniques, the study seeks to offer a more robust understanding of urban growth dynamics in Somalia. Additionally, the research supports Sustainable Development Goals (SDGs) 11 and 7, emphasizing the importance of developing inclusive, safe, and sustainable cities and ensuring access to reliable energy. Focusing on these objectives, the study seeks to improve residents' overall quality of life in Somalia's urban environments. Novelty of the Paper This paper introduces a novel approach to forecasting urban population growth in Somalia by integrating advanced statistical models, including ARIMA, TBATS, NNAR, and hybrid methodologies. The study aims to identify critical patterns and fluctuations by analyzing historical urban population data, offering more profound insights into the complexities of urbanization trends in Somalia. The innovative application of diverse and hybrid models enhances predictive accuracy, addressing a significant gap in the literature. The findings are designed to inform strategic decision-making for policymakers and urban planners, ultimately aiding in effective responses to the challenges posed by rapid urbanization in the region. Materials and methods Study area and source of data This study utilized historical data from 1961 to 2022, sourced from the World Bank Development Indicators, to forecast Somalia's urban population growth from 2023 to 2033. The analysis employed ARIMA, TBATS, NNAR, and hybrid models to forecast urban population growth in Somalia. The modelling process was conducted using R (version 4.1.3), ensuring a robust approach to predicting annual changes in the Somalia urban population. ARIMA Model An ARIMA model, characterized by the parameters p, d, and q, is constructed using historical values from the series {𝑌𝑡} along with random disturbances {∈𝑡}. The following equations typically represent this relationship. To separate the influence of previous observations from random errors, the model is modified by placing the autoregressive components on one side and the moving average components on the other. The values Φ𝑖​ indicate how past observations affect the current value, while Θ𝑖 represents how past errors influence the current value.[ 10 ] $$\:{\varvec{y}}_{\varvec{t}}\sum\:_{\varvec{i}=1}^{\varvec{p}}\mathbf{\varnothing\:}\mathbf{i}\:{\varvec{y}}_{\varvec{t}-\varvec{i}+\:\:}\sum\:_{\varvec{i}=1}^{\varvec{q}}\varvec{\Theta\:}\varvec{i}{\in\:}_{\varvec{t}-\varvec{i}+}{\in\:}_{\varvec{t}}$$ The ARIMA model fitting process involves several key steps, including checking for stationarity, estimating autoregressive (AR) and moving average (MA) parameters, conducting diagnostic checks, and making predictions. The Box-Jenkins method, which is effective for short-term forecasts, was utilized in this study to analyze Somalia's urban population growth from 1961 to 2022, using 62 data points to ensure accuracy. Stationarity was assessed through various statistical tests and plots, leading to the application of differencing to stabilize the data. The best AR and MA orders were determined using autocorrelation functions and expert judgment, while the model selection was guided by the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). Finally, the Ljung-Box test checked for serial correlation in residuals, and error metrics like RMSE, MAE, and MAPE evaluated the model's predictive performance. TBATS The TBATS (Trigonometric Seasonal, Box-Cox Transformation, ARMA Errors, Trend, and Seasonality) model is a versatile time series forecasting approach designed to accommodate different seasonality, trends, and error structures. It utilizes trigonometric functions to capture multiple seasonal patterns, applies a Box-Cox transformation to address non-constant variance, incorporates ARMA errors for modeling residuals, and includes trend components. The specific formula for the TBATS model can be intricate, depending on its configuration. $$\:{\varvec{Y}}^{\left(\varvec{\omega\:}\right)}={\varvec{i}}_{\varvec{t}-1+\:}\sum\:_{\varvec{t}=1}^{\varvec{T}}{\varvec{s}}_{\varvec{t}-{\varvec{m}}_{1\:\:}}^{\left(\varvec{i}\right)}+{\varvec{d}}_{\varvec{t}}$$ In this equation, y(ω)t​ signifies the observation after the Box-Cox transformation has been applied with parameter ω, while yt​ refers to the original observation at time t. The term lt​ represents the local level, ϕ indicates the damped trend, b denotes the long-run trend, and T reflects the seasonal pattern. The component (i)ti​ represents the i-th seasonal element, mi​ indicates the seasonal period, and dt​ corresponds to the residuals' ARMA(p, q) process. The TBATS model was identified using the tbats() function in the "forecast" package.[ 11 ] NNAR The NNAR (Neural Network Autoregressive) model is a time series forecasting approach that employs neural networks to identify patterns and relationships within the data. It integrates autoregressive elements with the non-linear features of neural networks to enhance forecasting precision. The specific formula for the NNAR model varies based on its architecture.[ 12 ] $$\:{y}_{t}={{\omega\:}}_{0}+\sum\:_{j=1}^{\:\text{Q}}{{\omega\:}}_{{g}^{g}}\:\:\:\:({{\omega\:}}_{oj\:}+\left(\sum\:_{j=1}^{\:\text{p}}{{\omega\:}}_{{j}^{y}}\:{y}_{t-1}\:\:\:\right)+{e}_{t}$$ Results Descriptive statistics Table 1 Descriptive statistics on the percentage of urban population growth in Somalia Mean SD Median Trimmed mean MAD Minimum Maximum Range skewness Kurtosis 30.85 8.01 29.83 30.58 7.66 17.31 46.73 29.42 0.31 -0.84 Table 1 presents the descriptive statistics for the percentage urban population growth in Somalia, revealing a mean growth rate of 30.85%, indicating a significant increase in urbanization. The standard deviation (SD) of 8.01 suggests variability in the growth rates, while the median of 29.83% shows that half of the observations fall below this value, reflecting a relatively symmetrical distribution. The trimmed mean of 30.58% and the mean absolute deviation (MAD) of 7.66 further emphasize the consistency of the growth rates, with a minimum of 17.31% and a maximum of 46.73%, resulting in a range of 29.42%. The skewness of 0.31 indicates a slight positive skew in the data, while the kurtosis of -0.84 suggests a relatively flat distribution compared to a normal distribution, indicating fewer extreme values. Stationarity Test The graph in Fig. 1 illustrates the trend of Somalia's urban population from 1961 to 2022. The non-linear pattern observed in the graph indicates that the time series data lacks stationarity. This suggests that population growth has experienced fluctuations rather than following a consistent trend, which is a critical consideration for accurate modeling and forecasting. As shown in Fig. 2 , the autocorrelation function (ACF) plot reveals a strong positive autocorrelation at lower lags, especially between lag one and lag 3, indicating a close relationship between past and current urban population growth values, which is essential for forecasting. As the lag increases, the ACF values gradually decline toward zero, suggesting that the impact of earlier observations weakens over time. The slight decrease in autocorrelation, with several values surpassing the upper confidence limit, points to possible non-stationarity in the series, emphasizing the necessity for differencing or other transformations before implementing ARIMA modelling. Figure 3 reveals the partial autocorrelation function (PACF) plot, which shows that the partial autocorrelation values are significantly positive at lag 1, indicating a strong direct relationship between the current value and its immediate past value. As the lags increase, the PACF values drop off quickly and remain close to zero for lags beyond 1, suggesting that the first lag largely explains any correlation at those lags. This pattern typically implies that the underlying time series may be well-represented by an autoregressive order 1 (AR(1)) model, with minimal contribution from higher-order lags. The confidence bands indicate that the significant correlation at lag 1 is statistically meaningful, while the subsequent lags fall within the bounds of randomness. Table 2 Test for stationarity at levels Test Test statistics p-value ADF original data -1.5653 0.7493 ADF(first differencing ) -4.5714 0.01 PPT (original data) -10.35 0.4946 PPT (first differencing ) -45.888 0.01 The results from Table 2 indicate the stationarity of the data at different levels, assessed using the Augmented Dickey-Fuller (ADF) and Phillips-Perron (PPT) tests. For the original data, the ADF test statistic is -1.5653 with a p-value of 0.7493, suggesting that we failed to reject the null hypothesis of non-stationarity, indicating that the original data is likely non-stationary. Similarly, the PPT test for the original data yields a test statistic of -10.35 and a p-value of 0.4946, reinforcing the conclusion of non-stationarity. However, upon first differencing, the ADF test statistic improves significantly to -4.5714 with a p-value of 0.01, allowing us to reject the null hypothesis and conclude that the first differenced data is stationary. The PPT test for the first differenced data shows an even more pronounced result with a test statistic of -45.888 and a p-value of 0.01, further confirming the stationarity of the series after differencing. These results indicate that while the original data is non-stationary, differencing the data successfully achieves stationarity, which is crucial for further time series analysis. Figure 4 illustrates the first differencing of Somalia's urban population from 1960 to 2022, highlighting fluctuations in growth rates. A sharp spike and subsequent drop around 2010 indicate a significant disruption in urban population trends. Following this volatility, the values stabilize around zero, suggesting a return to more consistent and stable growth rates in the years afterward. Table 3 Model selection P d Q AIC BIC 1 1 1 98.57439 104.3699 0 1 1 111.67282 115.5365 1 1 0 108.49454 112.3582 0 1 0 115.76290 117.6947 Source: Computed by the authors. ARIMA modeling was conducted using R version 4.3.1. Table 3 summarizes the results of the ARIMA model selection process, showcasing various combinations of parameters (P, d, Q) along with their corresponding Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) values. The ARIMA (1,1,1) model exhibits the lowest AIC (98.57439) and BIC (104.3699) values, indicating it provides the best fit for the data while balancing model complexity and goodness of fit. In contrast, the other models, including ARIMA (0,1,1), ARIMA (1,1,0), and ARIMA (0,1,0), have higher AIC and BIC values, suggesting they are less optimal for this dataset. Therefore, the ARIMA (1,1,1) model is recommended for further analysis based on these criteria. Figure 5 presents forecasts for Somalia's urban population using the ARIMA (1,1,1) model, indicating a steady upward trend from 1960 to 2022. The black line represents the historical data, while the shaded area around the forecast line illustrates the uncertainty in predictions for future growth. The forecast suggests a continued increase in urban population, projecting it to reach around 50 million by the early 2020s, reflecting a positive growth trajectory despite past fluctuations. Table 4 Error metrics for out-of-sample forecast RMSE MAE ME MAPE MASE Test set 0.6487 0.5657 0.5657 1.2571 0.9921 Source: World Bank Data, accessed (December 2024), Computation conducted using R software Table 4 presents the error metrics for the out-of-sample forecast, indicating the model's predictive performance on the test set. The Root Mean Square Error (RMSE) is 0.6487, suggesting a moderate prediction error level. At the same time, the Mean Absolute Error (MAE) of 0.5657 indicates the average magnitude of the forecast errors without considering their direction. The Mean Error (ME) is also reported as 0.5657, reflecting a slight prediction bias. The Mean Absolute Percentage Error (MAPE) of 1.2571 suggests the forecasts are relatively accurate, with errors expressed as a percentage of the actual values. Lastly, the Mean Absolute Scaled Error (MASE) of 0.9921 indicates that the model's performance is comparable to a naive forecasting method, suggesting that while the model is effective, there may still be room for improvement in accuracy. These metrics provide a comprehensive view of the model's forecasting capabilities, highlighting strengths and areas for potential enhancement (Table 4 ). Figure 6 illustrates the trends in urban population growth by displaying actual, fitted, and forecasted values derived from three time series models: ARIMA, NNAR, and TBATS. The x-axis represents the years, while the y-axis indicates the percentage of urban population growth. Each model's fitted values closely track the actual data points, demonstrating their effectiveness in capturing historical trends. The forecasted values extend beyond the observed data, providing insights into future urbanization trends. The comparison highlights the strengths and weaknesses of each model in accurately predicting urban growth patterns, which are essential for urban planning and policy-making (Fig. 6 ). Figure 7 presents a series of plots that compare the actual, fitted, and forecasted values of urban population growth using three hybrid models: ARIMA-TBATS, ARIMA-NNAR, and ARMIMA-TBATS-NNAR. Each subplot illustrates the model's performance over time, with the x-axis denoting the years and the y-axis indicating the percentage of urban population growth. The actual values serve as a benchmark, while the fitted values demonstrate how well each model captures historical trends. The forecasted values project future growth, allowing for an evaluation of each model's predictive capabilities. Notably, the proximity of fitted values to actual data suggests that the models are adept at capturing underlying patterns. However, variations in forecasted values may reveal differing levels of accuracy and reliability among the models in predicting future urbanization trends (Fig. 7 ). Table 4 Forecast performance of the single time series models, including ARIMA, TBATS, NNAR Model Theil’sU MAPE SMAPE RMSE ARIMA 1.1581 0.8627 0.0126 0.6486 TBATS 0.3239 0.2831 0.0028 0.1842 NNAR 0.6140 0.6951 0.0069 0.3341 Table 4 presents the forecast performance metrics for three single time series models: ARIMA, TBATS, and NNAR, evaluated using Theil's U, Mean Absolute Percentage Error (MAPE), Symmetric Mean Absolute Percentage Error (SMAPE), and Root Mean Square Error (RMSE). Among the models, TBATS demonstrates the best performance with the lowest values across all metrics, indicating superior accuracy and reliability in its forecasts, as evidenced by Theil's U of 0.3239, MAPE of 0.2831, SMAPE of 0.0028, and RMSE of 0.1842. In contrast, ARIMA shows the highest Theil's U at 1.1581, suggesting it may not be as effective in capturing the underlying data patterns. At the same time, NNAR falls in between with moderate performance metrics. TBATS emerges as the most effective model for forecasting in this analysis, highlighting its capability to provide more precise predictions than the other models (Table 4 ). Table 5 Forecast performance of the hybrid time series models, including ARIMA- TBATS, ARIMA- NNAR, ARIMA- TBATS- NNAR Model Theil’sU MAPE SMAPE RMSE ARIMA-TBATS 0.7270 0.7460 0.0075 0.4088 ARIMA-NNAR 0.4626 0.3842 0.0038 0.2633 ARIMA-TBATS-NNAR 0.2569 0.2513 0.0025 0.1456 Table 5 summarizes the forecast performance of three hybrid time series models: ARIMA-TBATS, ARIMA-NNAR, and ARIMA-TBATS-NNAR, evaluated using Theil's U, Mean Absolute Percentage Error (MAPE), Symmetric Mean Absolute Percentage Error (SMAPE), and Root Mean Square Error (RMSE). The ARIMA-TBATS-NNAR model exhibits the best performance overall, with the lowest Theil's U of 0.2569, MAPE of 0.2513, SMAPE of 0.0025, and RMSE of 0.1456, indicating its superior accuracy and effectiveness in capturing the underlying data patterns. The ARIMA-TBATS model performs moderately with a Theil's U of 0.7270 and higher error metrics. In contrast, the ARIMA-NNAR model performs better than ARIMA-TBATS but not as well as the combined model. This analysis highlights the advantages of a hybrid approach, as integrating multiple models improves forecasting accuracy and reliability (Table 5 ). Table 6 Forecast value of percentage of urban population growth during 2022 to 2031 using the best-fitted model (TBATS) Model Year Point Forecast 80% lower Higher 85% 95% lower 95% upper TBATS 2022 47.25209 46.35659 48.16489 45.88943 48.65521 TBATS 2023 47.76328 46.42849 49.13644 45.73706 49.87926 TBATS 2024 48.26571 46.55544 50.03880 45.67475 51.00363 TBATS 2025 48.75938 46.69967 50.90993 45.64479 52.08650 TBATS 2026 49.24431 46.84781 51.76340 45.62675 53.14869 TBATS 2027 49.72052 46.99361 52.60567 45.61114 54.20014 TBATS 2028 50.18805 47.13376 53.44026 45.59289 55.24633 TBATS 2029 50.64693 47.26638 54.26926 45.56914 56.29053 TBATS 2030 51.09720 47.39036 55.09399 45.53821 57.33480 TBATS 2031 51.53893 47.50508 55.91530 45.49911 58.38051 Table 6 presents the forecasted percentage of urban population growth from 2022 to 2031 using the TBATS model, which indicates a steady increase in urban population growth over the years. Starting at approximately 47.25% in 2022, the point forecast rises to about 51.54% by 2031. The accompanying confidence intervals show an 80% lower bound, an 85% higher bound, and a 95% lower and upper bound, reflecting the uncertainty in the predictions. For instance, in 2023, the point forecast is 47.76%, with a 95% confidence interval ranging from approximately 45.74–49.88%, suggesting that while growth is expected, there is variability in the actual outcomes. Overall, the data indicate a positive trend in urban population growth, with increasing confidence in the forecasts as the years progress (Table 6 ). . Table 7 Forecast values of the percentage of urban population growth during 2022 to 2031 using the best-fitted hybrid model (ARIMA- TBATS – NNAR) Model Year Point Forecast 80% lower Higher 85% 95% lower 95% upper ARIMA- TBATS- NNAR 2022 47.21197 46.35659 48.16489 45.88943 48.65521 ARIMA- TBATS- NNAR 2023 47.67688 46.42849 49.13644 45.73706 49.87926 ARIMA- TBATS- NNAR 2024 48.12628 46.55544 50.03880 45.67475 51.00363 ARIMA- TBATS- NNAR 2025 48.56059 46.69967 50.90993 45.64479 52.08650 ARIMA- TBATS- NNAR 2026 48.98041 46.84781 51.76340 45.62675 53.14869 ARIMA- TBATS- NNAR 2027 49.38645 46.99361 52.60567 45.61114 54.20014 ARIMA- TBATS- NNAR 2028 49.77952 47.13376 53.44026 45.59289 55.24633 ARIMA- TBATS- NNAR 2029 50.16048 47.26638 54.26926 45.56914 56.29053 ARIMA- TBATS- NNAR 2030 50.53020 47.39036 55.09399 45.53821 57.33480 ARIMA- TBATS- NNAR 2031 50.88955 47.50508 55.91530 45.49911 58.38051 Table 7 outlines the forecasted percentage of urban population growth from 2022 to 2031 using a hybrid model combining ARIMA, TBATS, and NNAR, indicating a consistent upward trend in urban population growth over the specified period. The point forecast begins at approximately 47.21% in 2022 and is projected to reach about 50.89% by 2031. The estimates are accompanied by confidence intervals, with the 95% lower and upper bounds providing a range of uncertainty around each point estimate. For example, in 2023, the point forecast is 47.68%, with a 95% confidence interval ranging from approximately 45.74–49.88%, suggesting a reliable growth expectation while acknowledging potential variability. Overall, the data reflect a positive trajectory in urban population growth, with increasing confidence in the forecasts as the years progress, indicating a significant demographic shift towards urbanization (Table 7 ). The figure illustrates the urbanization rate from 1960 to 2021, using three forecasting models: ARIMA, TBATS, and NNAR, all showing a consistent upward trend. Each model predicts a steady increase in urban population, suggesting ongoing urbanization as societies shift towards city living (Fig. 8 ). The figure presents a series of plots that compare the actual, fitted, and forecasted values of urban population growth using three distinct models: ARIMA-TBATS, ARIMA-NNAR, and ARMIMA-TBATS-NNAR. Each subplot illustrates the model's performance over time, with the x-axis denoting the years and the y-axis indicating the percentage of urban population growth. The actual values serve as a benchmark, while the fitted values demonstrate how well each model captures historical trends. The forecasted values project future growth, allowing for an evaluation of each model's predictive capabilities. Notably, the proximity of fitted values to actual data suggests that the models are adept at capturing underlying patterns. However, variations in forecasted values may reveal differing levels of accuracy and reliability among the models in predicting future urbanization trends (Fig. 9 ). Discussion This study aimed to investigate hybrid models to predict the percentage growth of the urban population. It tested six time series models, which included three single models (ARIMA, TBATS, NNAR) and three hybrid models, using data from 1960 to 2021. The findings indicated that among the single time series models, TBATS performed the best. In contrast, the hybrid model ARIMA-TBATS-NNAR emerged as the most effective mathematical model for forecasting urban population growth. This suggests that leveraging the strengths of ARIMA, TBATS, and NNAR models together leads to enhanced forecasting accuracy for urban population growth over the upcoming decade (2022–2031). The ARIMA (1, 1, 1) model was identified as the most appropriate choice for forecasting urban population growth in Somalia, owing to its effective balance between model fit and complexity while delivering dependable forecasts. The accuracy of the ARIMA (1, 1, 1) model, as indicated by its MAPE, RMSE, and MAE values, highlights its capability to generate reliable predictions with minimal error. This model's performance underscores its suitability for capturing the trends in urban population growth in Somalia. Our results are consistent with earlier research. The study conducted in Mexico found that ARIMA models produced relatively accurate population forecasts for Greater Mexico City, with a median error of 5.7% over a 10-year horizon, although estimates for the age group 65 + showed higher errors exceeding 20% in many municipalities.[ 13 ]. Another study conducted in Togo forecasts that Togo's total population will reach approximately 14.2 million by 2050 using the ARIMA (3, 2, 0) model, highlighting the need for strategic planning in response to this anticipated growth.[ 14 ]. Another study identified ARIMA (20, 1, 10) as the optimal model for forecasting urban population growth in the Philippines, predicting an increasing trend in urbanization over the next several years[ 15 ]. A study conducted in Indonesia, employed the ARIMA method to forecast the population growth in Indonesia, specifically predicting an increase of 17,947 residents in Madiun Regency from 2022 to 2024[ 16 ]. The study found that the ARIMA (1, 1, 0) model effectively predicts the population growth in Zhejiang Province, indicating a generally increasing population trend.[ 17 ]. In a study conducted in India forecasting India's population, the ARIMA (1, 2, 3) model was identified as the most appropriate, demonstrating significant coefficients for both autoregressive and moving average terms, indicating its effectiveness in predicting future population trends.[ 18 ]The study forecasts urban population trends in 210 prefecture-level cities in China using four models: the Malthusian model, Unary linear regression model, Logistic model, and Gray prediction model, with the Gray prediction model yielding the highest accuracy. Results indicate a shifting population dynamic, with middle-tier cities experiencing growth while high-tier and low-tier cities face declines, leading to an increasing population gap between cities[ 19 ]This study applies the Multi-layer Perceptron (MLP) based Artificial Neural Network-Markov Chain (ANN-Markov) model to forecast urban population growth in the Miami Metropolitan Area under three scenarios: business as usual, planned growth, and sustainable growth, while assessing the impacts of rising sea levels on flood risks.[ 20 ].This study utilizes convolutional neural networks (CNN) enhanced by Spider Monkey Optimization (SMO) to forecast urban population growth patterns in a specified area, yielding significant improvements in predictive accuracy and sustainability compared to conventional methods.[ 21 ]. This study forecasts urban population growth in the Kathmandu Valley by utilizing the MLP-ANN model, achieving a prediction accuracy of 93.82% while analyzing land use and land cover changes through 2041 under various sustainable development scenarios[ 22 ].The study forecasts urban population growth in Nagpur, Maharashtra, utilizing an artificial neural network-based cellular automata (CA-ANN) model, achieving an accuracy of 81.23% in predicting land use land cover changes up to 2025[ 23 ].The study forecasts urban population growth in Sleman Regency, Yogyakarta, Indonesia, using the CA-Markov chain model to predict a 15.48% increase in built-up areas by 2026 based on Landsat satellite imagery and the Normalized Difference Built-Up Index (NDBI).[ 24 ]. This study forecasts urban population growth in South Korea by utilizing an explainable artificial intelligence (XAI) model that integrates land-cover maps and various socioeconomic and environmental attributes to predict urban expansion trends influenced by proximity to developed areas and topographical features.[ 25 ]. Implications This research examines how predicted population rise in urban population growth the effects of anticipated urban population growth in Somali cities on policy-making, revealing that swift urbanization significantly affects Somalia. It highlights that unplanned urban expansion contributes to issues such as the displacement of people, inadequate solid waste management, and challenges related to economic, social, health, and environmental conditions. According to UN-Habitat, in 2018, urban residents comprised 45% of Somalia's population, with an urban growth rate of 4.23% from 2015 to 2020. The number of displaced individuals in Somalia surged from 1.10 million in 2017 to 2.60 million in 2018, representing an increase in the displaced population from 7–17% of the total. Additionally, there was a notable rise in returns from neighboring countries, with approximately 100,000 returnees registered in Somalia in 2018. Furthermore, 81.5% of the Somali population is under the age of 35, highlighting the youth's crucial role in promoting sustainable urban development in the country. The UN report on Somalia highlights that rapid and unplanned urbanization, influenced by landowners' interests and the needs of displaced communities, exacerbates clan dynamics and conflict, potentially increasing instability in cities. With the population expected to become predominantly urban after 2026, there is a critical opportunity for well-planned urbanization to foster economic diversification, social equality, and resilience through inclusive governance and urban planning. Conclusion This study emphasizes the application of ARIMA, TBATS, NNAR, and hybrid models to forecast urban population growth trends in Somalia, distinguishing it from existing research. The validated models effectively predict an increase in urban residents in Somalia from 2022 to 2033. Recognizing the potential opportunities and challenges posed by this anticipated growth, the study concludes that it is essential for the government and urban planners to develop tailored sustainable urban development strategies to effectively manage these changes Suggestions for Future Research Future research on forecasting urban population growth in Somalia could explore the integration of additional variables, such as economic indicators, migration patterns, and environmental factors, into the ARIMA, TBATS, NNAR, and hybrid models. This would enhance predictive accuracy and provide a more comprehensive understanding of the dynamics influencing urbanization. Additionally, comparative studies with other forecasting methods, including machine learning techniques, could be conducted to evaluate their effectiveness in predicting urban population trends. Engaging local stakeholders in the research process may also yield valuable insights and foster the development of more context-specific urban planning strategies. Furthermore, investigating the underlying causes of rapid urbanization in Somalia, focusing on factors such as economic opportunities, conflict displacement, and climate change impacts, could provide deeper insights into the drivers pushing populations toward urban areas. Declarations Ethical Considerations This study was based on the secondary analysis of publicly available, aggregated data from the World Bank Development Indicators (https://data.worldbank.org/indicator/SP.URB.TOTL.IN.Z) As the research did not involve direct interaction with human participants or the use of identifiable private information, formal ethics committee approval and participant consent were not required for this specific analysis. Consent to Participate: Not applicable for the reasons stated above. Consent for Publication: Not applicable as no individual data are presented in this manuscript. Funding: The authors declare that no external funding was received for this research. Competing interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Competing interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Data availability: The data analyzed in this study is publicly available from the World Bank database (https://data.worldbank.org/indicator/SP.URB.TOTL.IN.Z Author’s contributions: Ayan Husein Korse: Conceptualization, data analysis, methodology, writing - original draft. Hana Mahdi Dahir: Data collection, literature review, writing - review & editing. Moyazzem Hossain: Statistical analysis, model validation, writing - review & editing. Farduus Ibraahim Mohamed: Literature review, data validation, writing - review & editing. Mohamed Said Hassan: Project administration, supervision, writing - review & editing. References our world in Date, “No TitleUrbanization,” 2024, [Online]. Available: https://ourworldindata.org/urbanization#:~:text=More than half of the,now live in urban areas. Y. Zhou, A. C. G. Varquez, and M. Kanda, “High-resolution global urban growth projection based on multiple applications of the SLEUTH urban growth model,” Sci. Data , vol. 6, no. 1, pp. 1–10, 2019, doi: 10.1038/s41597-019-0048-z. G. Chen et al. , “Global projections of future urban land expansion under shared socioeconomic pathways,” Nat. Commun. , vol. 11, no. 1, pp. 1–12, 2020, doi: 10.1038/s41467-020-14386-x. K. Alsaadat, “European Journal of Science, Innovation and Technology EJSIT Artificial Intelligence in Education,” vol. 4, no. 1, p. 207, 2024, [Online]. Available: www.ejsit-journal.com K. Malarvizhi, S. V. Kumar, and P. Porchelvan, “Urban sprawl modelling and prediction using regression and Seasonal ARIMA: a case study for Vellore, India,” Model. Earth Syst. Environ. , vol. 8, no. 2, pp. 1597–1615, 2022, doi: 10.1007/s40808-021-01170-z. L. M. A. Bettencourt, “Urban growth and the emergent statistics of cities,” Sci. Adv. , vol. 6, no. 34, pp. 1–12, 2020, doi: 10.1126/sciadv.aat8812. UN- Habitat, “No TitleWorld Cities Report 2020: The Value of Sustainable Urbanization,” UN-Habitat. [Online]. Available: https://unhabitat.org/world-cities-report-2020-the-value-of-sustainable-urbanization A. A. Warsame, “The Impact of Urbanization on Energy Demand: An Empirical Evidence from Somalia,” Int. J. Energy Econ. Policy , vol. 12, no. 1, pp. 383–389, 2022, doi: 10.32479/ijeep.11823. X. Li et al. , “Global urban growth between 1870 and 2100 from integrated high resolution mapped data and urban dynamic modeling,” Commun. Earth Environ. , vol. 2, no. 1, pp. 1–10, 2021, doi: 10.1038/s43247-021-00273-w. R. Adolph, 済無 No Title No Title No Title . 2016. A. M. de Livera, R. J. Hyndman, and R. D. Snyder, “Forecasting time series with complex seasonal patterns using exponential smoothing,” J. Am. Stat. Assoc. , vol. 106, no. 496, pp. 1513–1527, 2011, doi: 10.1198/jasa.2011.tm09771. A. Maleki, S. Nasseri, M. S. Aminabad, and M. Hadi, “Comparison of ARIMA and NNAR Models for Forecasting Water Treatment Plant’s Influent Characteristics,” KSCE J. Civ. Eng. , vol. 22, no. 9, pp. 3233–3245, 2018, doi: 10.1007/s12205-018-1195-z. M. González-leonardo, N. Newsham, E. Baptista, and F. Rowe, “Assessing the accuracy of ARIMA models to forecast population at the intraurban level in Greater Mexico City,” pp. 1–23. T. Nyoni and M. Chipo, “Prediction of total population in Togo using ARIMA models,” Munich Pers. RePEc Arch. , no. 93983, 2019, [Online]. Available: https://mpra.ub.uni-muenchen.de/93983/ A. I. Numanovich and M. A. Abbosxonovich, “THE ANALYSIS OF LANDS IN SECURITY ZONES OF HIGH-VOLTAGE POWER LINES (POWER LINE) ON THE EXAMPLE OF THE FERGANA REGION PhD of Fergana polytechnic institute, Uzbekistan PhD applicant of Fergana polytechnic institute, Uzbekistan,” EPRA Int. J. Multidiscip. Res. (IJMR)-Peer Rev. J. , no. 2, pp. 198–210, 2020, doi: 10.36713/epra2013. Y. Farida, M. Farmita, N. Ulinnuha, and D. Yuliati, “Forecasting Population of Madiun Regency Using ARIMA Method,” CAUCHY J. Mat. Murni dan Apl. , vol. 7, no. 3, pp. 420–431, 2022, doi: 10.18860/ca.v7i3.16156. J. Dai and S. Chen, “The application of ARIMA model in forecasting population data,” J. Phys. Conf. Ser. , vol. 1324, no. 1, 2019, doi: 10.1088/1742-6596/1324/1/012100. M. Personal and R. Archive, “Munich Personal RePEc Archive Predicting total population in India : A Box-Jenkins ARIMA approach,” no. 92436, 2019. L. Chen, T. Mu, X. Li, and J. Dong, “Population Prediction of Chinese Prefecture-Level Cities Based on Multiple Models,” Sustain. , vol. 14, no. 8, pp. 1–23, 2022, doi: 10.3390/su14084844. G. W. Bazie and M. T. Adimassie, “Modern health services utilization and associated factors in North East Ethiopia,” PLoS One , vol. 12, no. 9, pp. 1–10, 2017, doi: 10.1371/journal.pone.0185381. T. S. & H. M. A. Mohammed Talib Abid, Njood Aljarrah, “No TitleForecasting and managing urban futures: machine learning models and optimization of urban expansion,” Asian J. Civ. Eng. , vol. 25, pp. 4673–4682, 2024, [Online]. Available: https://link.springer.com/article/10.1007/s42107-024-01072-2 Puja Bharti & Arindam Biswas, “No TitlePredicting Urban Growth of Kathmandu Valley Using Artificial Intelligence,” J. Geovisualization Spat. Anal. , vol. 8, no. 40, 2024, [Online]. Available: https://link.springer.com/article/10.1007/s41651-024-00201-4 B. D. & P. M. Farhan Khan, “No TitleUrban Growth Modeling and Prediction of Land Use Land Cover Change Over Nagpur City, India Using Cellular Automata Approach,” Geospatial Technol. Landsc. Environ. Manag. , pp. 261–282, 2022, [Online]. Available: https://link.springer.com/chapter/10.1007/978-981-16-7373-3_13 b nursida. arif@uny. ac. i. ∙ L. T. Nursida Arifa, “No TitleMonitoring and predicting development of built-up area in sub-urban areas: A case study of Sleman, Yogyakarta, Indonesia,” Heliyon , vol. 10, no. 14, 2024, [Online]. Available: https://www.cell.com/heliyon/fulltext/S2405-8440(24)10497-5 by M. K. andGeunhan Kim, “No TitleModeling and Predicting Urban Expansion in South Korea Using Explainable Artificial Intelligence (XAI) Model,” Appl. Sci. , vol. 12, no. 18, 2022, [Online]. Available: https://www.mdpi.com/2076-3417/12/18/9169 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6353211","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":454739317,"identity":"c7f98d35-7923-4397-8675-ad2ee1b285bf","order_by":0,"name":"Hana Mahdi Dahir","email":"","orcid":"","institution":"Amoud University","correspondingAuthor":false,"prefix":"","firstName":"Hana","middleName":"Mahdi","lastName":"Dahir","suffix":""},{"id":454739318,"identity":"2f3da879-10da-4e07-9583-fba1f1240a73","order_by":1,"name":"Ayan Husein Korse","email":"","orcid":"","institution":"Amoud 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12:38:27","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6353211/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6353211/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":82465045,"identity":"23372430-1703-4a42-83c5-da769fbb6192","added_by":"auto","created_at":"2025-05-11 16:03:18","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":17008,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eUrban population growth (annual %) in Somalia from 19961- 2022\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-6353211/v1/a43759eebc814a70fb996339.png"},{"id":82464878,"identity":"92f11274-f481-42a1-8150-c9ebeebb7922","added_by":"auto","created_at":"2025-05-11 15:55:18","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":12773,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eACF plot of urban population growth trends\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-6353211/v1/3fb7fd8b5ca4b9e4a2fe631a.png"},{"id":82465044,"identity":"b2645afc-a645-4840-8e59-01765271374d","added_by":"auto","created_at":"2025-05-11 16:03:18","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":12607,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePACF plot of urban population growth trends\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-6353211/v1/6324972fe2af0d1efe59d1a9.png"},{"id":82464875,"identity":"8a38ab0d-312c-411f-b360-32fe912e1221","added_by":"auto","created_at":"2025-05-11 15:55:18","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":16036,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDifferentiated urban population growth time series in Somalia\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-6353211/v1/d3a81562ab4b06b56d34c1de.png"},{"id":82464873,"identity":"bb14e803-e244-4bd4-b084-6d6e60e3da92","added_by":"auto","created_at":"2025-05-11 15:55:18","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":15678,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eARIMA (1, 1, 1)\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-6353211/v1/b62532a6d6ba1f84f86cff9c.png"},{"id":82464880,"identity":"7cdb38e4-f30c-4d0f-932b-98687b948756","added_by":"auto","created_at":"2025-05-11 15:55:18","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":357561,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eActual, fitted, and forecasted values from ARIMA, NNAR, and TBATS models, the x-axis and y-axis are the year and percentage of urban population growth\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6353211/v1/7cc72b5b72b4776cc6fca56c.jpeg"},{"id":82465048,"identity":"1e66ce81-8f79-44bf-b600-4e90493561f7","added_by":"auto","created_at":"2025-05-11 16:03:19","extension":"jpeg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":398894,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eActual, fitted, and forecasted values from ARIMA-TBATS, ARIMA-NNAR, and ARMIMA-TBATS-NNAR models. The x-axis and y-axis are the year and percentage of urban population growth.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage7.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6353211/v1/abc6ec2e5e6b81d1fae5e271.jpeg"},{"id":82464884,"identity":"709900f9-14f2-48ca-b922-40cd17a22ea5","added_by":"auto","created_at":"2025-05-11 15:55:18","extension":"jpeg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":293187,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eForecast percentage of population growth from ARIMA, TBATS, NNAR\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage8.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6353211/v1/7b665919075ca1b176482e8d.jpeg"},{"id":82465046,"identity":"834b86bb-b98c-4218-a16d-7fbdf9f5b824","added_by":"auto","created_at":"2025-05-11 16:03:18","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":16023,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eForecast percentage of population growth (blue line) from ARIMA- TBATS, ARIMA - NNAR, ARIMA- TBATS - NNAR\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-6353211/v1/0964dcd590866ee85a329816.png"},{"id":87765755,"identity":"49dd940a-d0c8-4f1f-aaec-2049a094af7a","added_by":"auto","created_at":"2025-07-28 18:01:35","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2297609,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6353211/v1/8325d213-cf6c-49b8-a43c-fda56cbafbc8.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Forecasting Urban Population Growth in Somalia: Using ARIMA, TBATS, NNAR, and Hybrid Models","fulltext":[{"header":"Introduction","content":"\u003cp\u003eUrbanization has led to over half of the world's population residing in densely populated urban areas, drastically altering lifestyles, work habits, transportation, and social networks. This significant shift, a recent development in human history, is explored through historical contexts, current patterns, and future projections.[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]The study predicts that global urban areas will continue to expand significantly, with forecasts indicating an increase from approximately 1.5\u0026nbsp;million square kilometers in 2018 to over 3\u0026nbsp;million square kilometers by 2100 under various Shared Socio-economic Pathways (SSPs). This growth is driven by population increase and economic development, with urban areas in regions like Asia, particularly China, expected to see the most substantial growth. [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]A study conducted in China and other Asian countries shows that land is projected to expand significantly. Estimates indicate that by 2100, urban areas will grow the largest under the SSP5 scenario, surpassing other scenarios. Urban population declines in regions like China may lead to a sharp decrease in urban land demand after the 2040s/2050s due to demographic changes. [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]\u003c/p\u003e \u003cp\u003eAnother study utilized the ARIMA (1, 1, 10) model to forecast urban population growth in Nigeria from 2023 to 2030, based on historical data from 1961 to 2022. The model demonstrated strong predictive accuracy, effectively capturing urbanization trends. The findings indicated a significant increase in Nigeria's urban population during the forecast period. [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. The application of Seasonal ARIMA (SARIMA) modeling in the study of urbanization growth in Vellore, India, indicated a significant increase in built-up density from 1991 to 2019, with predictions suggesting continued growth towards outer zones by 2045. The analysis revealed that built-up density decreases with increasing distance from the city center and major roads, highlighting a trend of urban expansion in less developed areas. [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Another study indicates a statistical dynamics framework for urbanization that incorporates agents' strategic behaviors to predict growth rates and emergent properties of cities, validated through simulations and analysis of 382 US Metropolitan Areas over nearly five decades.[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]Urbanization growth refers to developing urban areas that harness sustainable practices to enhance communities' economic, social, and environmental well-being while maintaining their unique identities. [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]\u003c/p\u003e \u003cp\u003eUrbanization in Somalia is rapidly increasing, with the urban population rising from about 30% in 1990 to over 50% by 2020, and projections suggest it could reach 60% by 2030. Mogadishu, the capital, has seen its population grow from approximately 1\u0026nbsp;million in 2000 to over 2.5\u0026nbsp;million in 2021. However, this urban growth presents challenges, particularly in energy supply, as only 36% of the population had access to electricity in 2019, significantly lower than in neighboring countries like Kenya and Ethiopia. [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. A high-resolution global dataset of urban dynamics from 1870 to 2100 was created as part of the study. This dataset reveals that urban growth under the SSP5 scenario has resulted in over a 40-fold increase in urban extent since 1870, providing valuable insights into the long-term environmental impacts of urbanization. The dataset includes detailed information on population growth, land use changes, and energy consumption, among other factors, and is a key resource for understanding the dynamics of urbanization in Somalia.\u003c/p\u003e \u003cp\u003eThe primary aim of this study is to establish a predictive model for urban population growth in Somalia by employing a combination of advanced statistical methods, including the Autoregressive Integrated Moving Average (ARIMA), TBATS, NNAR, and hybrid models. This comprehensive approach, backed by thorough research, enhances the accuracy of forecasts, providing critical insights for policymakers to effectively navigate the challenges posed by rapid urbanization, particularly regarding infrastructure and energy supply. By integrating multiple modeling techniques, the study seeks to offer a more robust understanding of urban growth dynamics in Somalia. Additionally, the research supports Sustainable Development Goals (SDGs) 11 and 7, emphasizing the importance of developing inclusive, safe, and sustainable cities and ensuring access to reliable energy. Focusing on these objectives, the study seeks to improve residents' overall quality of life in Somalia's urban environments.\u003c/p\u003e\n\u003ch3\u003eNovelty of the Paper\u003c/h3\u003e\n\u003cp\u003eThis paper introduces a novel approach to forecasting urban population growth in Somalia by integrating advanced statistical models, including ARIMA, TBATS, NNAR, and hybrid methodologies. The study aims to identify critical patterns and fluctuations by analyzing historical urban population data, offering more profound insights into the complexities of urbanization trends in Somalia. The innovative application of diverse and hybrid models enhances predictive accuracy, addressing a significant gap in the literature. The findings are designed to inform strategic decision-making for policymakers and urban planners, ultimately aiding in effective responses to the challenges posed by rapid urbanization in the region.\u003c/p\u003e"},{"header":"Materials and methods","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eStudy area and source of data\u003c/h2\u003e \u003cp\u003eThis study utilized historical data from 1961 to 2022, sourced from the World Bank Development Indicators, to forecast Somalia's urban population growth from 2023 to 2033. The analysis employed ARIMA, TBATS, NNAR, and hybrid models to forecast urban population growth in Somalia. The modelling process was conducted using R (version 4.1.3), ensuring a robust approach to predicting annual changes in the Somalia urban population.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eARIMA Model\u003c/h3\u003e\n\u003cp\u003eAn ARIMA model, characterized by the parameters p, d, and q, is constructed using historical values from the series {\u0026#119884;\u0026#119905;} along with random disturbances {\u0026isin;\u0026#119905;}. The following equations typically represent this relationship. To separate the influence of previous observations from random errors, the model is modified by placing the autoregressive components on one side and the moving average components on the other. The values Φ\u0026#119894;​ indicate how past observations affect the current value, while Θ\u0026#119894; represents how past errors influence the current value.[\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:{\\varvec{y}}_{\\varvec{t}}\\sum\\:_{\\varvec{i}=1}^{\\varvec{p}}\\mathbf{\\varnothing\\:}\\mathbf{i}\\:{\\varvec{y}}_{\\varvec{t}-\\varvec{i}+\\:\\:}\\sum\\:_{\\varvec{i}=1}^{\\varvec{q}}\\varvec{\\Theta\\:}\\varvec{i}{\\in\\:}_{\\varvec{t}-\\varvec{i}+}{\\in\\:}_{\\varvec{t}}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe ARIMA model fitting process involves several key steps, including checking for stationarity, estimating autoregressive (AR) and moving average (MA) parameters, conducting diagnostic checks, and making predictions. The Box-Jenkins method, which is effective for short-term forecasts, was utilized in this study to analyze Somalia's urban population growth from 1961 to 2022, using 62 data points to ensure accuracy. Stationarity was assessed through various statistical tests and plots, leading to the application of differencing to stabilize the data. The best AR and MA orders were determined using autocorrelation functions and expert judgment, while the model selection was guided by the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). Finally, the Ljung-Box test checked for serial correlation in residuals, and error metrics like RMSE, MAE, and MAPE evaluated the model's predictive performance.\u003c/p\u003e\n\u003ch3\u003eTBATS\u003c/h3\u003e\n\u003cp\u003eThe TBATS (Trigonometric Seasonal, Box-Cox Transformation, ARMA Errors, Trend, and Seasonality) model is a versatile time series forecasting approach designed to accommodate different seasonality, trends, and error structures. It utilizes trigonometric functions to capture multiple seasonal patterns, applies a Box-Cox transformation to address non-constant variance, incorporates ARMA errors for modeling residuals, and includes trend components. The specific formula for the TBATS model can be intricate, depending on its configuration.\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:{\\varvec{Y}}^{\\left(\\varvec{\\omega\\:}\\right)}={\\varvec{i}}_{\\varvec{t}-1+\\:}\\sum\\:_{\\varvec{t}=1}^{\\varvec{T}}{\\varvec{s}}_{\\varvec{t}-{\\varvec{m}}_{1\\:\\:}}^{\\left(\\varvec{i}\\right)}+{\\varvec{d}}_{\\varvec{t}}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn this equation, y(ω)t​ signifies the observation after the Box-Cox transformation has been applied with parameter ω, while yt​ refers to the original observation at time t. The term lt​ represents the local level, ϕ indicates the damped trend, b denotes the long-run trend, and T reflects the seasonal pattern. The component (i)ti​ represents the i-th seasonal element, mi​ indicates the seasonal period, and dt​ corresponds to the residuals' ARMA(p, q) process. The TBATS model was identified using the tbats() function in the \"forecast\" package.[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]\u003c/p\u003e\n\u003ch3\u003eNNAR\u003c/h3\u003e\n\u003cp\u003eThe NNAR (Neural Network Autoregressive) model is a time series forecasting approach that employs neural networks to identify patterns and relationships within the data. It integrates autoregressive elements with the non-linear features of neural networks to enhance forecasting precision. The specific formula for the NNAR model varies based on its architecture.[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$$\\:{y}_{t}={{\\omega\\:}}_{0}+\\sum\\:_{j=1}^{\\:\\text{Q}}{{\\omega\\:}}_{{g}^{g}}\\:\\:\\:\\:({{\\omega\\:}}_{oj\\:}+\\left(\\sum\\:_{j=1}^{\\:\\text{p}}{{\\omega\\:}}_{{j}^{y}}\\:{y}_{t-1}\\:\\:\\:\\right)+{e}_{t}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003eDescriptive statistics\u003c/h2\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDescriptive statistics on the percentage of urban population growth in Somalia\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"10\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMean\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSD\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMedian\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTrimmed mean\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMAD\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eMinimum\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eMaximum\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eRange\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eskewness\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eKurtosis\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e30.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e8.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e29.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e30.58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e7.66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e17.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e46.73\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e29.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-0.84\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e presents the descriptive statistics for the percentage urban population growth in Somalia, revealing a mean growth rate of 30.85%, indicating a significant increase in urbanization. The standard deviation (SD) of 8.01 suggests variability in the growth rates, while the median of 29.83% shows that half of the observations fall below this value, reflecting a relatively symmetrical distribution. The trimmed mean of 30.58% and the mean absolute deviation (MAD) of 7.66 further emphasize the consistency of the growth rates, with a minimum of 17.31% and a maximum of 46.73%, resulting in a range of 29.42%. The skewness of 0.31 indicates a slight positive skew in the data, while the kurtosis of -0.84 suggests a relatively flat distribution compared to a normal distribution, indicating fewer extreme values.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eStationarity Test\u003c/h3\u003e\n\u003cp\u003e \u003c/p\u003e \u003cp\u003eThe graph in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e illustrates the trend of Somalia's urban population from 1961 to 2022. The non-linear pattern observed in the graph indicates that the time series data lacks stationarity. This suggests that population growth has experienced fluctuations rather than following a consistent trend, which is a critical consideration for accurate modeling and forecasting.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, the autocorrelation function (ACF) plot reveals a strong positive autocorrelation at lower lags, especially between lag one and lag 3, indicating a close relationship between past and current urban population growth values, which is essential for forecasting. As the lag increases, the ACF values gradually decline toward zero, suggesting that the impact of earlier observations weakens over time. The slight decrease in autocorrelation, with several values surpassing the upper confidence limit, points to possible non-stationarity in the series, emphasizing the necessity for differencing or other transformations before implementing ARIMA modelling.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e reveals the partial autocorrelation function (PACF) plot, which shows that the partial autocorrelation values are significantly positive at lag 1, indicating a strong direct relationship between the current value and its immediate past value. As the lags increase, the PACF values drop off quickly and remain close to zero for lags beyond 1, suggesting that the first lag largely explains any correlation at those lags. This pattern typically implies that the underlying time series may be well-represented by an autoregressive order 1 (AR(1)) model, with minimal contribution from higher-order lags. The confidence bands indicate that the significant correlation at lag 1 is statistically meaningful, while the subsequent lags fall within the bounds of randomness.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eTest for stationarity at levels\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTest\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTest statistics\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ep-value\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eADF original data\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-1.5653\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.7493\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eADF(first differencing )\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-4.5714\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePPT (original data)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-10.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.4946\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePPT (first differencing )\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-45.888\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe results from Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e indicate the stationarity of the data at different levels, assessed using the Augmented Dickey-Fuller (ADF) and Phillips-Perron (PPT) tests. For the original data, the ADF test statistic is -1.5653 with a p-value of 0.7493, suggesting that we failed to reject the null hypothesis of non-stationarity, indicating that the original data is likely non-stationary. Similarly, the PPT test for the original data yields a test statistic of -10.35 and a p-value of 0.4946, reinforcing the conclusion of non-stationarity. However, upon first differencing, the ADF test statistic improves significantly to -4.5714 with a p-value of 0.01, allowing us to reject the null hypothesis and conclude that the first differenced data is stationary. The PPT test for the first differenced data shows an even more pronounced result with a test statistic of -45.888 and a p-value of 0.01, further confirming the stationarity of the series after differencing. These results indicate that while the original data is non-stationary, differencing the data successfully achieves stationarity, which is crucial for further time series analysis.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e illustrates the first differencing of Somalia's urban population from 1960 to 2022, highlighting fluctuations in growth rates. A sharp spike and subsequent drop around 2010 indicate a significant disruption in urban population trends. Following this volatility, the values stabilize around zero, suggesting a return to more consistent and stable growth rates in the years afterward.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eModel selection\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ed\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eQ\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAIC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eBIC\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e98.57439\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e104.3699\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e111.67282\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e115.5365\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e108.49454\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e112.3582\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e115.76290\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e117.6947\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eSource: Computed by the authors. ARIMA modeling was conducted using R version 4.3.1.\u003c/b\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e summarizes the results of the ARIMA model selection process, showcasing various combinations of parameters (P, d, Q) along with their corresponding Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) values. The ARIMA (1,1,1) model exhibits the lowest AIC (98.57439) and BIC (104.3699) values, indicating it provides the best fit for the data while balancing model complexity and goodness of fit. In contrast, the other models, including ARIMA (0,1,1), ARIMA (1,1,0), and ARIMA (0,1,0), have higher AIC and BIC values, suggesting they are less optimal for this dataset. Therefore, the ARIMA (1,1,1) model is recommended for further analysis based on these criteria.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e presents forecasts for Somalia's urban population using the ARIMA (1,1,1) model, indicating a steady upward trend from 1960 to 2022. The black line represents the historical data, while the shaded area around the forecast line illustrates the uncertainty in predictions for future growth. The forecast suggests a continued increase in urban population, projecting it to reach around 50\u0026nbsp;million by the early 2020s, reflecting a positive growth trajectory despite past fluctuations.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eError metrics for out-of-sample forecast\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eME\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMAPE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eMASE\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTest set\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.6487\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.5657\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.5657\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.2571\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9921\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eSource: World Bank Data, accessed (December 2024), Computation conducted using R software\u003c/h2\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e4\u003c/span\u003e presents the error metrics for the out-of-sample forecast, indicating the model's predictive performance on the test set. The Root Mean Square Error (RMSE) is 0.6487, suggesting a moderate prediction error level. At the same time, the Mean Absolute Error (MAE) of 0.5657 indicates the average magnitude of the forecast errors without considering their direction. The Mean Error (ME) is also reported as 0.5657, reflecting a slight prediction bias. The Mean Absolute Percentage Error (MAPE) of 1.2571 suggests the forecasts are relatively accurate, with errors expressed as a percentage of the actual values. Lastly, the Mean Absolute Scaled Error (MASE) of 0.9921 indicates that the model's performance is comparable to a naive forecasting method, suggesting that while the model is effective, there may still be room for improvement in accuracy. These metrics provide a comprehensive view of the model's forecasting capabilities, highlighting strengths and areas for potential enhancement (Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e illustrates the trends in urban population growth by displaying actual, fitted, and forecasted values derived from three time series models: ARIMA, NNAR, and TBATS. The x-axis represents the years, while the y-axis indicates the percentage of urban population growth. Each model's fitted values closely track the actual data points, demonstrating their effectiveness in capturing historical trends. The forecasted values extend beyond the observed data, providing insights into future urbanization trends. The comparison highlights the strengths and weaknesses of each model in accurately predicting urban growth patterns, which are essential for urban planning and policy-making (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e presents a series of plots that compare the actual, fitted, and forecasted values of urban population growth using three hybrid models: ARIMA-TBATS, ARIMA-NNAR, and ARMIMA-TBATS-NNAR. Each subplot illustrates the model's performance over time, with the x-axis denoting the years and the y-axis indicating the percentage of urban population growth. The actual values serve as a benchmark, while the fitted values demonstrate how well each model captures historical trends. The forecasted values project future growth, allowing for an evaluation of each model's predictive capabilities. Notably, the proximity of fitted values to actual data suggests that the models are adept at capturing underlying patterns. However, variations in forecasted values may reveal differing levels of accuracy and reliability among the models in predicting future urbanization trends (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eForecast performance of the single time series models, including ARIMA, TBATS, NNAR\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTheil\u0026rsquo;sU\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMAPE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSMAPE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eARIMA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.1581\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.8627\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0126\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.6486\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTBATS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.3239\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.2831\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0028\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.1842\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNNAR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.6140\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.6951\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0069\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.3341\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e4\u003c/span\u003e presents the forecast performance metrics for three single time series models: ARIMA, TBATS, and NNAR, evaluated using Theil's U, Mean Absolute Percentage Error (MAPE), Symmetric Mean Absolute Percentage Error (SMAPE), and Root Mean Square Error (RMSE). Among the models, TBATS demonstrates the best performance with the lowest values across all metrics, indicating superior accuracy and reliability in its forecasts, as evidenced by Theil's U of 0.3239, MAPE of 0.2831, SMAPE of 0.0028, and RMSE of 0.1842. In contrast, ARIMA shows the highest Theil's U at 1.1581, suggesting it may not be as effective in capturing the underlying data patterns. At the same time, NNAR falls in between with moderate performance metrics. TBATS emerges as the most effective model for forecasting in this analysis, highlighting its capability to provide more precise predictions than the other models (Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eForecast performance of the hybrid time series models, including ARIMA- TBATS, ARIMA- NNAR, ARIMA- TBATS- NNAR\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTheil\u0026rsquo;sU\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMAPE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSMAPE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eARIMA-TBATS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.7270\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.7460\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0075\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.4088\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eARIMA-NNAR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.4626\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.3842\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0038\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.2633\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eARIMA-TBATS-NNAR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.2569\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.2513\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0025\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.1456\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e5\u003c/span\u003e summarizes the forecast performance of three hybrid time series models: ARIMA-TBATS, ARIMA-NNAR, and ARIMA-TBATS-NNAR, evaluated using Theil's U, Mean Absolute Percentage Error (MAPE), Symmetric Mean Absolute Percentage Error (SMAPE), and Root Mean Square Error (RMSE). The ARIMA-TBATS-NNAR model exhibits the best performance overall, with the lowest Theil's U of 0.2569, MAPE of 0.2513, SMAPE of 0.0025, and RMSE of 0.1456, indicating its superior accuracy and effectiveness in capturing the underlying data patterns. The ARIMA-TBATS model performs moderately with a Theil's U of 0.7270 and higher error metrics. In contrast, the ARIMA-NNAR model performs better than ARIMA-TBATS but not as well as the combined model. This analysis highlights the advantages of a hybrid approach, as integrating multiple models improves forecasting accuracy and reliability (Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e5\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eForecast value of percentage of urban population growth during 2022 to 2031 using the best-fitted model (TBATS)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYear\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePoint Forecast\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e80% lower\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eHigher 85%\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e95% lower\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e95% upper\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTBATS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e47.25209\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e46.35659\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e48.16489\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e45.88943\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e48.65521\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTBATS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2023\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e47.76328\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e46.42849\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e49.13644\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e45.73706\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e49.87926\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTBATS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e48.26571\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e46.55544\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e50.03880\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e45.67475\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e51.00363\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTBATS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2025\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e48.75938\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e46.69967\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e50.90993\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e45.64479\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e52.08650\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTBATS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2026\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e49.24431\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e46.84781\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e51.76340\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e45.62675\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e53.14869\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTBATS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2027\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e49.72052\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e46.99361\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e52.60567\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e45.61114\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e54.20014\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTBATS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2028\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e50.18805\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e47.13376\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e53.44026\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e45.59289\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e55.24633\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTBATS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2029\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e50.64693\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e47.26638\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e54.26926\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e45.56914\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e56.29053\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTBATS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2030\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e51.09720\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e47.39036\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e55.09399\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e45.53821\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e57.33480\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTBATS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2031\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e51.53893\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e47.50508\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e55.91530\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e45.49911\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e58.38051\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e6\u003c/span\u003e presents the forecasted percentage of urban population growth from 2022 to 2031 using the TBATS model, which indicates a steady increase in urban population growth over the years. Starting at approximately 47.25% in 2022, the point forecast rises to about 51.54% by 2031. The accompanying confidence intervals show an 80% lower bound, an 85% higher bound, and a 95% lower and upper bound, reflecting the uncertainty in the predictions. For instance, in 2023, the point forecast is 47.76%, with a 95% confidence interval ranging from approximately 45.74\u0026ndash;49.88%, suggesting that while growth is expected, there is variability in the actual outcomes. Overall, the data indicate a positive trend in urban population growth, with increasing confidence in the forecasts as the years progress (Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e6\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab8\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eForecast values of the percentage of urban population growth during 2022 to 2031 using the best-fitted hybrid model (ARIMA- TBATS \u0026ndash; NNAR)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYear\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePoint Forecast\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e80% lower\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eHigher 85%\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e95% lower\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e95% upper\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eARIMA- TBATS- NNAR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e47.21197\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e46.35659\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e48.16489\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e45.88943\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e48.65521\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eARIMA- TBATS- NNAR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2023\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e47.67688\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e46.42849\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e49.13644\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e45.73706\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e49.87926\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eARIMA- TBATS- NNAR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e48.12628\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e46.55544\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e50.03880\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e45.67475\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e51.00363\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eARIMA- TBATS- NNAR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2025\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e48.56059\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e46.69967\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e50.90993\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e45.64479\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e52.08650\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eARIMA- TBATS- NNAR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2026\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e48.98041\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e46.84781\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e51.76340\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e45.62675\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e53.14869\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eARIMA- TBATS- NNAR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2027\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e49.38645\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e46.99361\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e52.60567\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e45.61114\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e54.20014\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eARIMA- TBATS- NNAR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2028\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e49.77952\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e47.13376\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e53.44026\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e45.59289\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e55.24633\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eARIMA- TBATS- NNAR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2029\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e50.16048\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e47.26638\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e54.26926\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e45.56914\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e56.29053\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eARIMA- TBATS- NNAR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2030\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e50.53020\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e47.39036\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e55.09399\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e45.53821\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e57.33480\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eARIMA- TBATS- NNAR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2031\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e50.88955\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e47.50508\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e55.91530\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e45.49911\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e58.38051\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e7\u003c/span\u003e outlines the forecasted percentage of urban population growth from 2022 to 2031 using a hybrid model combining ARIMA, TBATS, and NNAR, indicating a consistent upward trend in urban population growth over the specified period. The point forecast begins at approximately 47.21% in 2022 and is projected to reach about 50.89% by 2031. The estimates are accompanied by confidence intervals, with the 95% lower and upper bounds providing a range of uncertainty around each point estimate. For example, in 2023, the point forecast is 47.68%, with a 95% confidence interval ranging from approximately 45.74\u0026ndash;49.88%, suggesting a reliable growth expectation while acknowledging potential variability. Overall, the data reflect a positive trajectory in urban population growth, with increasing confidence in the forecasts as the years progress, indicating a significant demographic shift towards urbanization (Table\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e7\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe figure illustrates the urbanization rate from 1960 to 2021, using three forecasting models: ARIMA, TBATS, and NNAR, all showing a consistent upward trend. Each model predicts a steady increase in urban population, suggesting ongoing urbanization as societies shift towards city living (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe figure presents a series of plots that compare the actual, fitted, and forecasted values of urban population growth using three distinct models: ARIMA-TBATS, ARIMA-NNAR, and ARMIMA-TBATS-NNAR. Each subplot illustrates the model's performance over time, with the x-axis denoting the years and the y-axis indicating the percentage of urban population growth. The actual values serve as a benchmark, while the fitted values demonstrate how well each model captures historical trends. The forecasted values project future growth, allowing for an evaluation of each model's predictive capabilities. Notably, the proximity of fitted values to actual data suggests that the models are adept at capturing underlying patterns. However, variations in forecasted values may reveal differing levels of accuracy and reliability among the models in predicting future urbanization trends (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eThis study aimed to investigate hybrid models to predict the percentage growth of the urban population. It tested six time series models, which included three single models (ARIMA, TBATS, NNAR) and three hybrid models, using data from 1960 to 2021. The findings indicated that among the single time series models, TBATS performed the best. In contrast, the hybrid model ARIMA-TBATS-NNAR emerged as the most effective mathematical model for forecasting urban population growth. This suggests that leveraging the strengths of ARIMA, TBATS, and NNAR models together leads to enhanced forecasting accuracy for urban population growth over the upcoming decade (2022\u0026ndash;2031).\u003c/p\u003e \u003cp\u003eThe ARIMA (1, 1, 1) model was identified as the most appropriate choice for forecasting urban population growth in Somalia, owing to its effective balance between model fit and complexity while delivering dependable forecasts. The accuracy of the ARIMA (1, 1, 1) model, as indicated by its MAPE, RMSE, and MAE values, highlights its capability to generate reliable predictions with minimal error. This model's performance underscores its suitability for capturing the trends in urban population growth in Somalia. Our results are consistent with earlier research. The study conducted in Mexico found that ARIMA models produced relatively accurate population forecasts for Greater Mexico City, with a median error of 5.7% over a 10-year horizon, although estimates for the age group 65\u0026thinsp;+\u0026thinsp;showed higher errors exceeding 20% in many municipalities.[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Another study conducted in Togo forecasts that Togo's total population will reach approximately 14.2\u0026nbsp;million by 2050 using the ARIMA (3, 2, 0) model, highlighting the need for strategic planning in response to this anticipated growth.[\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Another study identified ARIMA (20, 1, 10) as the optimal model for forecasting urban population growth in the Philippines, predicting an increasing trend in urbanization over the next several years[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eA study conducted in Indonesia, employed the ARIMA method to forecast the population growth in Indonesia, specifically predicting an increase of 17,947 residents in Madiun Regency from 2022 to 2024[\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. The study found that the ARIMA (1, 1, 0) model effectively predicts the population growth in Zhejiang Province, indicating a generally increasing population trend.[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. In a study conducted in India forecasting India's population, the ARIMA (1, 2, 3) model was identified as the most appropriate, demonstrating significant coefficients for both autoregressive and moving average terms, indicating its effectiveness in predicting future population trends.[\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]The study forecasts urban population trends in 210 prefecture-level cities in China using four models: the Malthusian model, Unary linear regression model, Logistic model, and Gray prediction model, with the Gray prediction model yielding the highest accuracy. Results indicate a shifting population dynamic, with middle-tier cities experiencing growth while high-tier and low-tier cities face declines, leading to an increasing population gap between cities[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]This study applies the Multi-layer Perceptron (MLP) based Artificial Neural Network-Markov Chain (ANN-Markov) model to forecast urban population growth in the Miami Metropolitan Area under three scenarios: business as usual, planned growth, and sustainable growth, while assessing the impacts of rising sea levels on flood risks.[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].This study utilizes convolutional neural networks (CNN) enhanced by Spider Monkey Optimization (SMO) to forecast urban population growth patterns in a specified area, yielding significant improvements in predictive accuracy and sustainability compared to conventional methods.[\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. This study forecasts urban population growth in the Kathmandu Valley by utilizing the MLP-ANN model, achieving a prediction accuracy of 93.82% while analyzing land use and land cover changes through 2041 under various sustainable development scenarios[\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e].The study forecasts urban population growth in Nagpur, Maharashtra, utilizing an artificial neural network-based cellular automata (CA-ANN) model, achieving an accuracy of 81.23% in predicting land use land cover changes up to 2025[\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e].The study forecasts urban population growth in Sleman Regency, Yogyakarta, Indonesia, using the CA-Markov chain model to predict a 15.48% increase in built-up areas by 2026 based on Landsat satellite imagery and the Normalized Difference Built-Up Index (NDBI).[\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. This study forecasts urban population growth in South Korea by utilizing an explainable artificial intelligence (XAI) model that integrates land-cover maps and various socioeconomic and environmental attributes to predict urban expansion trends influenced by proximity to developed areas and topographical features.[\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e].\u003c/p\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003eImplications\u003c/h2\u003e \u003cp\u003eThis research examines how predicted population rise in urban population growth the effects of anticipated urban population growth in Somali cities on policy-making, revealing that swift urbanization significantly affects Somalia. It highlights that unplanned urban expansion contributes to issues such as the displacement of people, inadequate solid waste management, and challenges related to economic, social, health, and environmental conditions. According to UN-Habitat, in 2018, urban residents comprised 45% of Somalia's population, with an urban growth rate of 4.23% from 2015 to 2020. The number of displaced individuals in Somalia surged from 1.10\u0026nbsp;million in 2017 to 2.60\u0026nbsp;million in 2018, representing an increase in the displaced population from 7\u0026ndash;17% of the total. Additionally, there was a notable rise in returns from neighboring countries, with approximately 100,000 returnees registered in Somalia in 2018. Furthermore, 81.5% of the Somali population is under the age of 35, highlighting the youth's crucial role in promoting sustainable urban development in the country. The UN report on Somalia highlights that rapid and unplanned urbanization, influenced by landowners' interests and the needs of displaced communities, exacerbates clan dynamics and conflict, potentially increasing instability in cities. With the population expected to become predominantly urban after 2026, there is a critical opportunity for well-planned urbanization to foster economic diversification, social equality, and resilience through inclusive governance and urban planning.\u003c/p\u003e \u003c/div\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThis study emphasizes the application of ARIMA, TBATS, NNAR, and hybrid models to forecast urban population growth trends in Somalia, distinguishing it from existing research. The validated models effectively predict an increase in urban residents in Somalia from 2022 to 2033. Recognizing the potential opportunities and challenges posed by this anticipated growth, the study concludes that it is essential for the government and urban planners to develop tailored sustainable urban development strategies to effectively manage these changes\u003c/p\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003eSuggestions for Future Research\u003c/h2\u003e \u003cp\u003eFuture research on forecasting urban population growth in Somalia could explore the integration of additional variables, such as economic indicators, migration patterns, and environmental factors, into the ARIMA, TBATS, NNAR, and hybrid models. This would enhance predictive accuracy and provide a more comprehensive understanding of the dynamics influencing urbanization. Additionally, comparative studies with other forecasting methods, including machine learning techniques, could be conducted to evaluate their effectiveness in predicting urban population trends. Engaging local stakeholders in the research process may also yield valuable insights and foster the development of more context-specific urban planning strategies. Furthermore, investigating the underlying causes of rapid urbanization in Somalia, focusing on factors such as economic opportunities, conflict displacement, and climate change impacts, could provide deeper insights into the drivers pushing populations toward urban areas.\u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eEthical Considerations\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study was based on the secondary analysis of publicly available, aggregated data from the World Bank Development Indicators (https://data.worldbank.org/indicator/SP.URB.TOTL.IN.Z)\u003c/p\u003e\n\u003cp\u003eAs the research did not involve direct interaction with human participants or the use of identifiable private information, formal ethics committee approval and participant consent were not required for this specific analysis.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent to Participate:\u003c/strong\u003e Not applicable for the reasons stated above.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for Publication:\u003c/strong\u003e Not applicable as no individual data are presented in this manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding:\u003c/strong\u003e The authors declare that no external funding was received for this research.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests:\u003c/strong\u003e The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests:\u003c/strong\u003e The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability:\u003c/strong\u003e The data analyzed in this study is publicly available from the World Bank database (https://data.worldbank.org/indicator/SP.URB.TOTL.IN.Z\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor\u0026rsquo;s contributions:\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003eAyan Husein Korse: Conceptualization, data analysis, methodology, writing - original draft.\u003c/li\u003e\n \u003cli\u003eHana Mahdi Dahir: Data collection, literature review, writing - review \u0026amp; editing.\u003c/li\u003e\n \u003cli\u003eMoyazzem Hossain: Statistical analysis, model validation, writing - review \u0026amp; editing.\u003c/li\u003e\n \u003cli\u003eFarduus Ibraahim Mohamed: Literature review, data validation, writing - review \u0026amp; editing.\u003c/li\u003e\n \u003cli\u003eMohamed Said Hassan: Project administration, supervision, writing - review \u0026amp; editing.\u003c/li\u003e\n\u003c/ul\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eour world in Date, \u0026ldquo;No TitleUrbanization,\u0026rdquo; 2024, [Online]. 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Available: https://www.mdpi.com/2076-3417/12/18/9169\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Urban Population Growth, Forecasting, Time Series Analysis, ARIMA, TBATS, NNAR, Hybrid Models, Somalia, Urban Planning, Sustainable Development Goals","lastPublishedDoi":"10.21203/rs.3.rs-6353211/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6353211/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eRapid urbanization presents opportunities and challenges, particularly in developing nations like Somalia. Accurate forecasting of urban population growth is essential for effective urban planning and resource management. This study employs ARIMA, TBATS, NNAR, and hybrid models to forecast urban population growth in Somalia, utilizing historical data from 1961 to 2022 sourced from the World Bank. The analysis evaluates the performance of single models and hybrid combinations (ARIMA-TBATS, ARIMA-NNAR, ARIMA-TBATS-NNAR) based on metrics including Theil\u0026rsquo;s U statistic, MAPE, SMAPE, and RMSE. Results indicate that the TBATS model best fits among the single time-series models, while the ARIMA-TBATS-NNAR hybrid model outperforms the others in forecasting urban population growth. The validated models effectively predict an increase in urban residents in Somalia from 2022 to 2033. This study underscores the importance of leveraging advanced statistical modeling, particularly hybrid approaches, to inform evidence-based strategies and optimize resource allocation for sustainable urban development in Somalia, contributing to achieving Sustainable Development Goals (SDGs) 11 and 7 and instilling hope for a more sustainable future.\u003c/p\u003e","manuscriptTitle":"Forecasting Urban Population Growth in Somalia: Using ARIMA, TBATS, NNAR, and Hybrid Models","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-05-11 15:55:13","doi":"10.21203/rs.3.rs-6353211/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"25d168ab-1df8-4dc3-bb95-1839424da512","owner":[],"postedDate":"May 11th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-07-28T17:53:27+00:00","versionOfRecord":[],"versionCreatedAt":"2025-05-11 15:55:13","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6353211","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6353211","identity":"rs-6353211","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}