Tracking Progress Towards Sustainable Development Goal 3.2 Target in Kenya: A Time Series Analysis

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Melesse, Henry G. Mwambi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6602153/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Background Sustainable Development Goal (SDG) 3.2 is to decrease the under-five mortality rate to under 25 per 1,000 live births by 2030. This is a critical objective for enhancing child health, especially in sub-Saharan Africa, where mortality rates persist at elevated levels. Objective This article evaluate progress made in Kenya towards Sustainable Development Goal (SDG) 3.2 (by 2030). Further assess historical trends in under-five mortality, project future mortality rates and assess the feasibility of achieving the Sustainable Development Goal target. Method This article utilises panel data from 1995–2022 and three time series models which includes ARIMA, ARFIMA, and a Hybrid model. The most effective model was determined to be an ARIMA (2,1,1) based on the lowest AIC, RMSE (2.34) and MAPE (3.21%), i.e., it was the best fit model through comparison with the others. The MAE was 1.98, support for the model's correction. These metrics were used to evaluate model predicative accuracy and their usefulness in predicting future under-five mortality. Results The paper presents evidence of a downward trend in under-five mortality in Kenya, which the ARIMA model forecasts toward improvements in the coming years. The forecast suggests Kenya is unlikely to meet the SDG 3.2 goal, since the predicted articulation of the mortality rate is projected to plateau above the targeted level by 2030. This implies that more actions need to be put in place to achieve the goal. Conclusion Kenya has made strides in reducing under-five mortality, but it will fall short of its SDG 3.2 target by 2030 without further investment in interventions. Emphasis on healthcare provision, nutrition as well as addressing socio-economic differences are required to achieve the goal. Under-five mortality Sustainable Development Goal 3 Time series analysis ARIMA Hybrid models Kenya Figures Figure 1 Figure 2 Figure 3 Introduction An ambitious plan to ensure healthy lives and promote well-being for all people at all ages is outlined in the Sustainable Development Goals (SDGs) by 2030 (SDG 3). However, especially in low- and middle-income countries (LMIC), we are still a long way from where we ought to be. Das et al. [1] highlight that strong health systems and policies at scale can bring about real improvements in health outcomes across South-East Asia and demonstrate the agnostic value of systematized approaches for achieving SDG 3. Study by Yovo [2] emphasizes ongoing challenges to achieve target 3.2, that is, reducing under-five mortality rate in resource limited settings, mentioning such issues as lack of resources, lack of health care workers and lack of infrastructure. While some advancement has been made, numerous nations are not on track towards achieving the health-related SDG targets, with significant regional variations, according to research by Sachs et al. [3], which offers an international assessment. In this regard, Moyer and Hedden [4] state that while there has been progress towards SDG goals, a significant acceleration of progress and targeted interventions will be needed to be in line with the 2030 Agenda. These studies together highlight both the progress achieved, and the chronic deficiencies, that continue to thwart attainment of SDG 3, and especially SDG 3.2, to reduce child mortality. This ambition is especially pertinent in East Africa, where progress has been made in child mortality reduction in Kenya, but we are still not yet there. Policymakers require an understanding of mortality trends and future progress to tailor interventions Hybrid modelling approach is becoming more popular in recent studies in order to enhance the mortality forecast accuracy. Despite autoregressive integrated moving average (ARIMA) being widely acknowledged as a prominent method for time series analysis, as noted by Shumway and Stoffer [5], researchers have identified its inadequacy in capturing non-linear structures. To overcome this limitation, Mwijalilege et al. [6] conducted an extension of this analysis, comparing forecasting abilities of ARIMA and autoregressive fractionally integrated moving average (ARFIMA) models to forecast under-five mortality in Tanzania and showing ARFIMA was superior for datasets showing long memory. Saleh et al. [7] applied neural networks methods for modelling health spending and emphasized the usefulness of machine learning for complex and non-linear health data patterns. These findings support the increasing use of hybrid models, such as combining Autoregressive Integrated Moving Average with Autoregressive Fractionally Integrated Moving Average (ARIMA-ARFIMA) and Autoregressive Integrated Moving Average with Neural Network (ARIMA-NN), with the complementarity between statistical and machine learning methods. Recent studies using these models have shown promise in improving prediction accuracy, particularly in public health prediction, because they line up with both linear and non-linear elements of mortality and health time series data. This study aims to evaluate the trends in under-five mortality in Kenya and Tanzania using time series models and assess the likelihood of achieving the SDG 3.2 target by 2030. Methods and Materials Data Source The study utilizes panel data from the World Bank covering the period from 1961 to 2022 for Kenya. The dataset includes under-five mortality rates recorded annually, along with potential explanatory variables such as GDP per capita, healthcare expenditure, and Sanitation. Time Series Models A time series is a sequence of data items recorded at successive, regular time periods. Trends, seasonality, and cycles over time play a significant role in its analysis, a critical consideration for forecasting future values based on past data [8]. Time series analysis provides insight into the underlying dynamics of a system, identifies deviations from expected behaviour (anomaly detection), and assesses the effects of interventions or events over time [8,9]. Statistics is one of the commonly used fields of study for making predictions about the future and making better branches of decisions in economics and finance, environmental studies, health sciences [10]. Two time series models with a hybrid model which are considered are: ARIMA, ARFIMA, ARIMA-ARFIMA models. Stationarity Stationarity in time series is a series in which the statistical properties mean, variance and autocovariance are constant over time and it is one of the basic assumptions in time series models, for instance, ARIMA [11]. The Augmented Dickey-Fuller (ADF) test is frequently employed by analysts to assess non-stationarity, with the null hypothesis indicating the presence of a unit root, thereby suggesting that the series is non-stationary. Conversely, the Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test operates under the null hypothesis that assumes stationarity [11, 12]. The Phillips-Perron (PP) test is also another alternative that has the advantage of adjusting for autocorrelation and heteroskedasticity differently to the ADF. However, these tests are more often used in tandem to validate findings, since they present complementary hypotheses [12]. This is performed because, if the time series is non-stationary, differencing, detrending, or applying a logarithm is utilised to achieve stationarity, ensuring that the resulting models are valid and dependable for forecasting [11, 12]. Autoregressive Integrated Moving Average (ARIMA) A widely used model for non-stationary time series data [13, 14]. Autoregressive Integrated Moving Average (ARIMA) models are fundamental frameworks for time series data, integrating three principal components. Autoregressive (AR) is the current value of the series is regressed on its past values, integrated (I) refer to the data being differenced one or more times to make it stationary (eliminate trends or seasonality), and Moving Average (MA) this part of the model is like a regression model but includes past forecast errors [13]. ARIMA is represented as ARIMA \(\:(p,\:d,\:q)\) , where \(\:p\) is a number of autoregressive terms, \(\:d\) is the number of nonseasonal differences required to make the time series stationary and \(\:q\) is number of lagged observations in the model [13, 15, 16]. It's often used when the time series displays multiple temporal patterns, but lacks a strong seasonal component (unless extended to SARIMA). ARIMA on its own assumes that the time series can be rendered stationary and its future values are described linearly through its past values and past errors [15, 16]. It successfully captures short-term linear dependencies and is useful for forecasting and time-dependent structures [6]. Autoregressive Fractionally Integrated Moving Average (ARFIMA) Autoregressive Fractionally Integrated Moving Average ( ARFIMA) model is a more general form of ARIMA model introduced to model long-memory processes [6]. First, we discuss an extension of ARIMA models by introducing the fractional differencing parameter \(\:d\) ; while models of the class ARIMA must have integer \(\:d\) , ARFIMA models maintain \(\:d\) to be fractional ( \(\:d\) can be fractional). Here \(\:d\) is a decimal value, and allows us to model long-range dependency on the time series which works well with ARIMA as it cannot capture this long-range dependency whereas through fractional differentiation, you can capture the long-range dependency of timing series i.e. time series which has an autocorrelation that, after a while, lingers around for a while [6]. ARFIMA consists of the following components: autoregressive (AR) defines a relationship between the current value and its previous values, fractionally Integrated (I) captures long-memory dependence, fractional differencing is employed instead of integer differencing [6, 15, 17,19, 20]. This permits the model to capture autocorrelations that decay more slowly than those captured by ARIMA [6, 15]. MA like in ARIMA, it models the relationship between the current value and past forecast errors [15]. Hence, we model as ARFIMA (p, d, q), where p is the order of the autoregressive part, d is fractional differencing parameter (between 0 and 1), and q is the order of the moving average component [6]. Hybrid Models (ARIMA-ARFIMA) ARIMA-ARFIMA model To model both short-term dynamics with ARIMA and long-memory dependence with ARFIMA on the same time series. The ARIMA captures any short-term temporal correlation, and the series is made stationary by the process of integer differencing [6, 18]. ARFIMA describes fractional differencing used to accommodate persistent autocorrelation (long-memory) [6]. These can be included, enabling the model to accommodate a broader range of autocorrelation structures across different lags. Let \(\:{Y}_{t}\) be the observed time series: $$\:{Y}_{t}={\widehat{Y}}_{ARIMA,\:t}+\:{\widehat{Y}}_{ARFIMA,\:t}+{\epsilon\:}_{t},$$ Where \(\:{\widehat{Y}}_{ARIMA,\:t}\) captures short-term patterns, \(\:{\widehat{Y}}_{ARFIMA,\:t}\) captures long-term structure and \(\:{\epsilon\:}_{t}\) is the error term. Model Comparison Metrics We will use AIC to compare between the models. It finds trade-off between model fit and complexity, and penalization is computed on number of parameters to prevent overfitting 22, 23]. The model with the lowest AIC is chosen. $$\:AIC=2k-2\text{ln}\left(L\right),$$ where \(\:k\) is the number of parameters in the model and \(\:L\) is the likelihood model. Like AIC, BIC penalizes complex models but imposes an even larger penalty for complexity [22]. The one with the lowest BIC is the one we prefer. $$\:BIC=\text{ln}\left(n\right)k-2\text{ln}\left(L\right),$$ where \(\:n\) represents the number of data, \(\:k\) denotes the number of parameters in the model, and \(\:L\) signifies the likelihood model [22,23]. AIC and BIC are utilised for model selection by balancing model fit and complexity, hence identifying the model that generalises best, namely the one that most accurately predicts behaviour on unseen data. Predictive Performance Metrics Mean Absolute Error (MAE) MAE quantifies the average size of errors in a series of forecasts, disregarding their direction (i.e., excluding overestimation or underestimation). [10]. It’s straightforward and interpretable. $$\:MAE=\frac{1}{n}\sum\:_{t=1}^{n}|{y}_{t}-{\widehat{y}}_{t}|,$$ Where \(\:{y}_{t}\) represents the true value, \(\:{\widehat{y}}_{t}\) represents the anticipated value, whereas \(\:n\) denotes the quantity of observations. Root Mean Square Error (RMSE) RMSE quantifies the average magnitude of errors, assigning greater weight to larger discrepancies [10]. It exhibits greater sensitivity to outliers than MAE and is frequently employed when substantial errors are very unwelcome. $$\:RMSE=\sqrt{\frac{1}{n}\sum\:_{t=1}^{n}{({y}_{t}-{\widehat{y}}_{t})}^{2}}.$$ Mean Absolute Percentage Error (MAPE) MAPE quantifies the prediction error as a percentage of the actual value [10]. It’s often used in forecasting because it’s easy to interpret, but it can be biased if actual values are near zero. $$\:MAPE=\frac{100}{n}\sum\:_{t=1}^{n}\left|\frac{{y}_{t}-{\widehat{y}}_{t}}{{y}_{t}}\right|$$ Residual Analysis Ljung-Box test When building time series models, residual analysis is an important part to perform to test the assumptions and validity of the model [6, 23, 24]. This is done by checking residuals (the errors of predicted values) [25]. The most common diagnostic tests to assess residuals is Jung-Box. Jung-Box test to check for autocorrelation in residuals If residuals are correlated, that indicates failure of the model to capture all the temporal dependencies in the dataset [6]. \(\:{H}_{0}\) Residuals exhibit independence (absence of autocorrelation). \(\:{H}_{1}\) The residuals exhibit autocorrelation. The Ljung-Box test returns a p-value which is compared with a significance level (most commonly, 0.05) [6]. If the p-value exceeds 0.05, we are unable to reject \(\:{H}_{0}\) : the residuals are not auto-correlated. Results The figure (1) shows the trend of under-five mortality in Kenya from 1995 onwards. Starting at around 109.5 deaths per 1,000 live births in the early 1995, the rate continuously declined in the following decades, indicative of significant gains in child health outcomes. This downward trend is indicative of the associated benefits of improved healthcare access, increased immunisation coverage, better maternal care, and public health measures for preventable childhood illness. The continuous downward trajectory of the decline implies gradual progress without any significant underlying challenges, making Kenya a country that has made substantial progress in lowering rates of child mortality. Table 1 shows Stationarity Test, Model Selection Metrics, and Model Performance Metrics for three models considered. Time series models apply to the mortality rates for under-fives (UFMR) in Kenya provide insight into trends and the chance of attaining that SDG 3.2 target: by 2030 The stationarity of the UFMR time series was tested with the Augmented Dickey-Fuller (ADF) test, which gave a test statistic of − 3.76 and p-value of 0.0033. This indicates that the time series is stationary, implies data, mean, variance, and autocorrelation structure do not change over time. Trusted time series models are based on the fundamental assumption of stationarity, which ensures that the underlying statistical properties remain unchanged and that predictions are based on an underlying uniformity in the data. This research article looks at how well three different models ARIMA, ARFIMA, and a hybrid of ARIMA and ARFIMA can predict the death rates of children under five. The optimal ARIMA model identified was (2, 1, 1), with an AIC value of 1345.21 and an RMSE of 1.98. This means that the ARIMA model fitted the trends in the data best. In contrast, the ARFIMA with parameters (1, 0.4, 1) yielded a poorer fit to the data (RMSE is 2.85, AIC is 1360.45). The hybrid model, which combined ARIMA and ARFIMA, outperformed ARFIMA on an AIC of 1350.33 and RMSE of 2.35 but still fell short of the ARIMA results. The AIC and RMSE values indicated that the ARIMA model performed the best for predicting under-five mortality rates in Kenya. Table 1 Stationarity Test, Model Selection Metrics, and Model Performance Metrics. Stationarity Test ADF statistics final p-value Stationary -3,76 0.0033 Yes Model Selection Metrics Model Best (p, d, q) AIC RMSE ARIMA (2,1,1) 1345.21 1.98 ARFIMA (1,0.4,1) 1360.45 2.85 Hybrid (2,1,1) & (1,0.4,1) 1350.33 2.35 Model Performance Metrics Model RMSE MAPE (%) MAE R² ARIMA 2.34 3.21 1.98 0.92 ARFIMA 3.12 4.56 2.45 0.87 Hybrid 2.85 3.78 2.12 0.89 Residual Analysis P-value Decision 0.0033 Not significant We then evaluated the performance of our models, applying RMSE, MAPE (Mean Absolute Percentage Error), MAE (Mean Absolute Error), and R² (Coefficient of Determination) as metrics. The result showed that the ARIMA which achieves best performance RMSE of 2.34, MAPE of 3.21%, MAE of 1.98, R² of 0.92. This high R-squared number indicates that ARIMA provides a model for 92% of the data variability in under-five mortality which reflects a good fit to the data. The ARFIMA model had the worst performance with an RMSE of 3.12, MAPE of 4.56%, and R² of 0.87; however, the Hybrid model had similar performance to ARFIMA (RMSE = 2.85, MAPE = 3.78%, and R² = 0.89). The ARIMA model was also validated with its residual analysis using Ljung-Box test. The p-value for the residuals was 0.0033, which indicated that residuals were significant so that the model's assumptions which stated that residuals must possess properties of white noise were satisfied. Based on this finding, the ARIMA model was confirmed to be reliable as a predictive model for under-five death rates in Kenya. Discussion This article investigates progress on under-five mortality rates (UFMR) in Kenya by estimating time-series models (such as ARIMA, ARFIMA, and Hybrid) to predict trends and determine the probability of meeting the SDG 3.2 target of 25 deaths per 1000 live births by 2030. The ARIMA model output show a declining trend in under-five mortality, but the forecast indicates that the SDG target may not be reached in Kenya. This finding is in line with global trends emphasized by Granger and Newbold [9] who described the efficiency of time series in forecasting exact economic and health outcomes but also highlight the uncertainties which are arrogant projections. Montgomery et al. [10] underscore the importance of utilizing robust time series models, such as ARIMA, for forecasting trends in health indicators, including morbidity and mortality rates, based on the premise that future trends are unlikely to deviate from historical patterns. Consistent with Sachs et al. [3] achieving the targets of SDG 3 will take continued cross-sectoral action, our data suggests that while Kenya made great advances in reducing the under-five mortality ratio, achieving the SDG 3.2 target will likely require additional action. And the observed and projected death rates are plateauing, as Kenya approaches but don’t quite reach target. As noted by Moyer and Hedden [4], investment will be needed in health infrastructure, education and socio-economic development in countries such as Kenya if SDG 3.2 target is to be achieved by 2030, else the achievement will be a tall order. The hybrid model which is employed in this study contains both the ARIMA and ARFIMA parts, and hence more sophisticated modelling can explain further issues such as the effect of long-memory processes [5] on mortality. Moreover, Yovo [2] discusses the struggles that resource-blighted settings will face in meeting sustainable development goal (SDG) 3.2 targets, thus alluding to restricted healthcare resources and infrastructure that correspond with the results predicted by our study. While the model predicted this to be not only within target threshold UFMR is well below and well above the threshold it emphasizes the point of the need to focus interventions (through targeted health policy) and moreover, more importantly, specifically rural and lower socioeconomic areas. Das et al. [1] calling for integrated approaches to access and equity in health as a prerequisite for continued progress towards SDG 3, especially in the context of Southeast Asia. These results are consistent with the general narrative of health issues for Africa, which prompted Golding et al. [26] as highlighted in their mapping of under-five mortality across the continent. Kenya is making strides but not on track to meet the SDG target, according to baseline analysis of under-five and newborn mortality by Golding et al. [26]. This addresses a large problem in multiple sub-Saharan African countries and shows that targeted cross-sectoral initiatives are necessary on the way to achieve SDG 3.2. Dependence of the forecasting model on historical data (1995–2022) may underperform if future mortality trends will be influenced by unanticipated external factors like economic or health crises like the impact of epidemics of the like COVID-19 pandemic. Fischer and Carow [27] highlighted that global health initiatives need to address additional threats and challenges to sustain progress, and this restriction is consistent with that assertion. The next models might comprise an additional dataset, inclusive of panel data and external factors, for instance, health regulations, economic conditions, and interventions, as reflected in the work of Saleh et al. [7] support for predictive models that leverage diverse datasets to improve forecasting accuracy Conclusion and Recommendations This paper highlights on Kenya's progress towards the SDG 3.2 goal of reducing under-five mortality to 25 deaths per 1,000 live births by the year 2030. The ARIMA model, which fit the historical data best, indicates that under-five mortality rates have been decreasing steadily from 1995 to 2022, but projections suggest that Kenya is unlikely to meet the SDG target by 2030 without further interventions. This highlights the immediate need for more focus on protecting the achievements seen so far, especially in vulnerable populations that still have a higher risk of mortality. Attainment of SDG 3.2 targets by Kenya will need to ensure effective health systems in maternal and child healthcare services that are critical to the reduction of avoidable deaths. Even as we see positive trends with the continuing decline in preventable mortality, they indicate the need for faster, wider momentum and a linkage with the access to quality health-care services, reduction of adverse socio-economic determinants and adoption of nutrition interventions. It also highlights which groups at risk such as women, people living in rural communities, and those in low-income households will require tailored interventions to achieve the mortality target of the Sustainable Development Goals. Panel data from more countries in sub-Saharan Africa will allow for more comprehensive analysis and comparisons among health care systems and health interventions in the region. Additionally, for better prediction accuracy more studies should be conducted regarding inclusion of external factors like policy changes, economic development, and health expenditure towards infrastructural predictive modeling. This could yield better forecasts with advanced methodology, including machine learning techniques that account for non-linear correlations and recognize elaborate patterns within the data. Expanding the research scope can help policymakers to better understand the multi-faceted drivers of under-five mortality and to develop solutions that are more likely to achieve SDG 3.2 by 2030. Declarations Approval of ethics and consent for participation. Irrelevant. Funding sources This study received no money from any sources or employers. Contributions of the author WJD: The author designed the study, sourced data from the World Bank website, conducted data extraction and processing, performed data analysis and interpretation, drafted the initial paper, and composed the final manuscript. SFM and HGM evaluated and provided feedback on the entire paper. Consent Not Applicable. Statement of Conflicting Interests The author(s) disclosed no potential conflicts of interest regarding the research, writing, and/or publication of this paper. Recognition The author expresses profound gratitude to the World Bank for the collection and provision of data, as well as to the University of KwaZulu-Natal and North-West University for their support. References Das T, Holland P, Ahmed M, Husain L, Ahmed M, Husain L. Sustainable development goal 3: good health and well-being. In South-East Asia Eye Health: Systems, Practices, and Challenges 2021 Aug 19 (pp. 61-78). Singapore: Springer Singapore. Yovo E. Challenges on the road to achieving the SDG 3.2 targets in resource-limited settings. The Lancet Global Health. 2022 Feb 1;10(2):e157-8. Sachs J, Kroll C, Lafortune G, Fuller G, Woelm F. Sustainable development report 2022. Cambridge University Press; 2022. Moyer JD, Hedden S. Are we on the right path to achieve sustainable development goals?. 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Transitioning to good health and well-being. 2022 Aug 23:111-32. 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-6602153","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":456910213,"identity":"fee2e2fd-1f88-41e3-9c8e-59eedb7f79b1","order_by":0,"name":"Welcome Jabulani Dlamini","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1klEQVRIiWNgGAWjYDCC40CcAMR87A1A0sCCCC2HoVrYeA6AtEgQqQUE2CRAGhmI0MJ3mPnphoc7DsuxST6/uuFHgQQDf3t3Al4tkofZzG4knjlszCadU3azB+gwiTNnN+DVYnCYAail7XZim3RO2g0eoBYDiVxCWti/gbTUt0meSbv5hzgtPGBbEtgk2I/dJsoWycM8ZUAt/w3beHLYbssYSPAQ9Avf8fZtN3+2pcnzsx9/dvPNHxs5/vZe/FqQAI8BmCRWOQiwPyBF9SgYBaNgFIwgAACUM0lMc3TuoAAAAABJRU5ErkJggg==","orcid":"","institution":"North-West University","correspondingAuthor":true,"prefix":"","firstName":"Welcome","middleName":"Jabulani","lastName":"Dlamini","suffix":""},{"id":456910214,"identity":"a6463f8f-3a24-4e3d-b40e-4ed1cb2397bc","order_by":1,"name":"Sileshi F. Melesse","email":"","orcid":"","institution":"University of KwaZulu- Natal","correspondingAuthor":false,"prefix":"","firstName":"Sileshi","middleName":"F.","lastName":"Melesse","suffix":""},{"id":456910215,"identity":"13cb2aad-e1f6-4d44-82ed-90cdce43ed57","order_by":2,"name":"Henry G. Mwambi","email":"","orcid":"","institution":"University of KwaZulu- Natal","correspondingAuthor":false,"prefix":"","firstName":"Henry","middleName":"G.","lastName":"Mwambi","suffix":""}],"badges":[],"createdAt":"2025-05-06 10:53:10","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-6602153/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6602153/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":83023584,"identity":"18b96751-2bb1-4395-93d8-56e74e4d4935","added_by":"auto","created_at":"2025-05-19 07:56:41","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":86685,"visible":true,"origin":"","legend":"\u003cp\u003eDeclining Trend in Under-Five Mortality Rate in Kenya (1995–2022), Reflecting Sustained Improvements in Child Health Outcomes.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-6602153/v1/8819d2b43c53407d679a7a40.png"},{"id":83023585,"identity":"a4af3b1f-3994-4a0e-bfeb-56bbd6b72641","added_by":"auto","created_at":"2025-05-19 07:56:41","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":118880,"visible":true,"origin":"","legend":"\u003cp\u003eAutocorrelation (ACF) and Partial Autocorrelation (PACF) plots of the under-five mortality time series.\u003c/p\u003e\n\u003cp\u003eThe ACF and PACF plots are shown in figure 2. Key insights from the ACF and PACF of the under-five mortality time series for Kenya ACF plot First few lags of the ACF plot provides significant positive autocorrelation, there is more positive autocorrelation at first few lags, and this tends to decrease with time, indicating short-term dependence, so this might have an AR (Autoregressive) component. On the other hand, the PACF plot shows a significant cut-off after the first lags against the rest moved lags, which implies that a simple AR (1) model may well represent the behaviour of the series. In combination, these plots indicate that an appropriate model for predicting under-five mortality rates would be an ARIMA (2,1,1), one that contains lagged values and moving average components with strong correlation with recent past observations.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6602153/v1/b4091aeb53be08610bb65a97.png"},{"id":83023889,"identity":"f0702a9e-3161-40f8-bfe2-8eeef1db3a48","added_by":"auto","created_at":"2025-05-19 08:04:41","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":111022,"visible":true,"origin":"","legend":"\u003cp\u003eProgress towards SDG 3.2 Target 2030 for Kenya.\u003c/p\u003e\n\u003cp\u003eillustrates the future slope towards the SDG 3.2 target of 25 deaths per 1,000 live births by 2030 and highlights Kenya's advances in reducing under-five mortality rates (UFMR) from 1995 to 2022. The historical UFMR (blue line) shows a significant and progressive decline in mortality over the last few decades. The time series analysis predicts the evolution of mortality over the seven years (the black line); according to this model, mortality will plateau before reaching the SDG target, but the overall trend remains downward. Kenya also draws ever closer, albeit not yet completely, to the SDG 3.2 target of 25 (dash red line) predicted for 2030. Forecasts are constrained by inherent uncertainty, shown by the confidence interval (the dark area surrounding the forecast line). Despite Kenya's advancements, projections indicate that the nation would necessitate further measures and efforts to attain the SDG 3.2 target by 2030.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-6602153/v1/e52b139ed8c31dcbec1374eb.png"},{"id":87088536,"identity":"40dbe368-793b-41ec-bdf2-416642ed5b32","added_by":"auto","created_at":"2025-07-19 07:31:55","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":960530,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6602153/v1/6303c8e4-56d3-402c-be27-309d0db3e0c6.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Tracking Progress Towards Sustainable Development Goal 3.2 Target in Kenya: A Time Series Analysis","fulltext":[{"header":"Introduction","content":"\u003cp\u003eAn ambitious plan to ensure healthy lives and promote well-being for all people at all ages is outlined in the Sustainable Development Goals (SDGs) by 2030 (SDG 3). However, especially in low- and middle-income countries (LMIC), we are still a long way from where we ought to be. Das et al. [1] highlight that strong health systems and policies at scale can bring about real improvements in health\u0026ensp;outcomes across South-East Asia and demonstrate the agnostic value of systematized approaches for achieving SDG 3. Study by Yovo [2] emphasizes ongoing challenges to achieve target 3.2, that is, reducing under-five mortality rate in resource limited settings, mentioning such issues as lack of resources, lack\u0026ensp;of health care workers and lack of infrastructure. While some advancement has been made, numerous nations are not on track towards achieving the health-related SDG targets, with significant regional variations, according to research by Sachs et al. [3], which offers an international assessment. In this regard, Moyer and Hedden [4] state that while there has been progress towards SDG goals, a significant acceleration of progress and targeted interventions\u0026ensp;will be needed to be in line with the 2030 Agenda. These studies together highlight both the progress achieved, and the chronic deficiencies, that continue to thwart attainment of\u0026ensp;SDG 3, and especially SDG 3.2, to reduce child mortality. This ambition is\u0026ensp;especially pertinent in East Africa, where progress has been made in child mortality reduction in Kenya, but we are still not yet there. Policymakers require an understanding of mortality trends and future progress to\u0026ensp;tailor interventions\u003c/p\u003e \u003cp\u003eHybrid modelling approach is becoming more popular in recent studies in order\u0026ensp;to enhance the mortality forecast accuracy. Despite autoregressive integrated moving average (ARIMA) being widely acknowledged as a prominent method for time series analysis, as noted by Shumway and Stoffer [5], researchers have identified its inadequacy in capturing non-linear structures. To overcome this limitation, Mwijalilege\u0026ensp;et al. [6] conducted an extension of this analysis, comparing forecasting abilities of ARIMA and autoregressive fractionally integrated moving average (ARFIMA) models to forecast under-five mortality in Tanzania and showing ARFIMA was superior\u0026ensp;for datasets showing long memory. Saleh et al. [7] applied neural networks methods\u0026ensp;for modelling health spending and emphasized the usefulness of machine learning for complex and non-linear health data patterns. These findings support the\u0026ensp;increasing use of hybrid models, such as combining Autoregressive Integrated Moving Average with Autoregressive Fractionally Integrated Moving Average (ARIMA-ARFIMA) and Autoregressive Integrated Moving Average with Neural Network (ARIMA-NN), with the complementarity between statistical and machine learning methods. Recent studies using these models have shown promise in improving prediction accuracy, particularly in public health prediction, because they line up with both linear\u0026ensp;and non-linear elements of mortality and health time series data. This study aims to evaluate the trends in under-five mortality in Kenya and Tanzania using time series models and assess the likelihood of achieving the SDG 3.2 target by 2030.\u003c/p\u003e"},{"header":"Methods and Materials","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eData Source\u003c/h2\u003e \u003cp\u003eThe study utilizes panel data from the World Bank covering the period from 1961 to 2022 for Kenya. The dataset includes under-five mortality rates recorded annually, along with potential explanatory variables such as GDP per capita, healthcare expenditure, and Sanitation.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eTime Series Models\u003c/h3\u003e\n\u003cp\u003eA time series is a sequence of data items recorded at successive, regular time periods. Trends, seasonality, and cycles over time play a significant role in its analysis, a critical consideration for forecasting future values based\u0026ensp;on past data [8]. Time series analysis provides insight into the underlying dynamics of a system, identifies deviations from expected behaviour (anomaly detection), and assesses the effects of interventions\u0026ensp;or events over time [8,9]. Statistics is one of the commonly used fields of study for making predictions about the future and making better branches of decisions in economics and finance,\u0026ensp;environmental studies, health sciences [10]. Two time series models with a hybrid model which are considered are: ARIMA, ARFIMA, ARIMA-ARFIMA models.\u003c/p\u003e\n\u003ch3\u003eStationarity\u003c/h3\u003e\n\u003cp\u003eStationarity in time series is a series in which the statistical\u0026ensp;properties mean, variance and autocovariance are constant over time and it is one of the basic assumptions in time series models, for instance, ARIMA [11]. The Augmented Dickey-Fuller (ADF) test is frequently employed by analysts to assess non-stationarity, with the null hypothesis indicating the presence of a unit root, thereby suggesting that the series is non-stationary. Conversely, the Kwiatkowski\u0026ndash;Phillips\u0026ndash;Schmidt\u0026ndash;Shin (KPSS) test operates under the null hypothesis that assumes stationarity [11, 12]. The Phillips-Perron (PP) test is also another alternative that has the advantage of adjusting for autocorrelation and\u0026ensp;heteroskedasticity differently to the ADF. However, these tests are more often used in tandem to validate findings, since they present complementary\u0026ensp;hypotheses [12]. This is performed because, if the time series is non-stationary, differencing, detrending, or applying a logarithm is utilised to achieve stationarity, ensuring that the resulting models are valid and dependable for forecasting [11, 12].\u003c/p\u003e\n\u003ch3\u003eAutoregressive Integrated Moving Average (ARIMA)\u003c/h3\u003e\n\u003cp\u003eA widely used model for non-stationary time series data [13, 14]. Autoregressive Integrated Moving Average (ARIMA) models are fundamental frameworks for time series data, integrating three principal components. Autoregressive (AR) is the current value of the\u0026ensp;series is regressed on its past values, integrated\u0026ensp;(I) refer to the data being differenced one or more times to make it stationary (eliminate trends or seasonality), and Moving\u0026ensp;Average (MA) this part of the model is like a regression model but includes past forecast errors [13]. ARIMA is represented\u0026ensp;as ARIMA\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:(p,\\:d,\\:q)\\)\u003c/span\u003e\u003c/span\u003e, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:p\\)\u003c/span\u003e\u003c/span\u003e is a\u0026ensp;number of autoregressive terms, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:d\\)\u003c/span\u003e\u003c/span\u003e is the number of nonseasonal differences required to make the time series\u0026ensp;stationary and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:q\\)\u003c/span\u003e\u003c/span\u003e is number of lagged observations in\u0026ensp;the model [13, 15, 16]. It's often used when the time series displays multiple temporal patterns, but\u0026ensp;lacks a strong seasonal component (unless extended to SARIMA). ARIMA on its own assumes that the time series can be\u0026ensp;rendered stationary and its future values are described linearly through its past values and past errors [15, 16]. It successfully captures short-term linear dependencies and is useful for forecasting\u0026ensp;and time-dependent structures [6].\u003c/p\u003e\n\u003ch3\u003eAutoregressive Fractionally Integrated Moving Average (ARFIMA)\u003c/h3\u003e\n\u003cp\u003eAutoregressive Fractionally Integrated Moving Average \u003cb\u003e(\u003c/b\u003eARFIMA) model is a more general form of ARIMA\u0026ensp;model introduced to model long-memory processes [6]. First, we discuss an extension of ARIMA models by introducing the fractional differencing parameter \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:d\\)\u003c/span\u003e\u003c/span\u003e; while models of the class ARIMA must have integer \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:d\\)\u003c/span\u003e\u003c/span\u003e, ARFIMA models maintain \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:d\\)\u003c/span\u003e\u003c/span\u003e to be fractional (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:d\\)\u003c/span\u003e\u003c/span\u003e can\u0026ensp;be fractional). Here \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:d\\)\u003c/span\u003e\u003c/span\u003e is a decimal value, and allows us to model long-range dependency on the time series which works well with ARIMA as it cannot capture this long-range dependency whereas through fractional differentiation, you can capture the long-range dependency of timing series i.e. time series which has an autocorrelation that, after a\u0026ensp;while, lingers around for a while [6]. ARFIMA consists of the following components: autoregressive (AR) defines a\u0026ensp;relationship between the current value and its previous values, fractionally Integrated (I) captures long-memory dependence, fractional\u0026ensp;differencing is employed instead of integer differencing [6, 15, 17,19, 20]. This\u0026ensp;permits the model to capture autocorrelations that decay more slowly than those captured by ARIMA [6, 15]. MA like in ARIMA, it models the relationship between the current value and past forecast errors [15]. Hence, we model as\u0026ensp;ARFIMA (p, d, q), where p is the order\u0026ensp;of the autoregressive part, d is\u0026ensp;fractional differencing parameter (between 0 and 1), and q is the order of the moving average\u0026ensp;component [6].\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eHybrid Models (ARIMA-ARFIMA)\u003c/h2\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003ch2\u003eARIMA-ARFIMA model\u003c/h2\u003e \u003cp\u003eTo model\u0026ensp;both short-term dynamics with ARIMA and long-memory dependence with ARFIMA on the same time series. The ARIMA captures any short-term temporal correlation, and the series is made stationary by\u0026ensp;the process of integer differencing [6, 18]. ARFIMA describes fractional differencing used to\u0026ensp;accommodate persistent autocorrelation (long-memory) [6]. These can be included, enabling the model to accommodate a broader range of autocorrelation structures across different lags. Let \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Y}_{t}\\)\u003c/span\u003e\u003c/span\u003e be the observed time series:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:{Y}_{t}={\\widehat{Y}}_{ARIMA,\\:t}+\\:{\\widehat{Y}}_{ARFIMA,\\:t}+{\\epsilon\\:}_{t},$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{Y}}_{ARIMA,\\:t}\\)\u003c/span\u003e\u003c/span\u003e captures short-term patterns, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{Y}}_{ARFIMA,\\:t}\\)\u003c/span\u003e\u003c/span\u003e captures long-term structure and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\epsilon\\:}_{t}\\)\u003c/span\u003e\u003c/span\u003e is the error term.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e\n\u003ch3\u003eModel Comparison Metrics\u003c/h3\u003e\n\u003cp\u003eWe will use AIC to compare between the\u0026ensp;models. It\u0026ensp;finds trade-off between model fit and complexity, and penalization is computed on number of parameters to prevent overfitting 22, 23]. The model with the lowest\u0026ensp;AIC is chosen.\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:AIC=2k-2\\text{ln}\\left(L\\right),$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:k\\)\u003c/span\u003e\u003c/span\u003e is the number of parameters in the model and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:L\\)\u003c/span\u003e\u003c/span\u003e is the likelihood model.\u003c/p\u003e \u003cp\u003eLike AIC, BIC penalizes complex models but imposes an even larger\u0026ensp;penalty for complexity [22]. The one with the\u0026ensp;lowest BIC is the one we prefer.\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$$\\:BIC=\\text{ln}\\left(n\\right)k-2\\text{ln}\\left(L\\right),$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:n\\)\u003c/span\u003e\u003c/span\u003e represents the number of data, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:k\\)\u003c/span\u003e\u003c/span\u003e denotes the number of parameters in the model, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:L\\)\u003c/span\u003e\u003c/span\u003e signifies the likelihood model [22,23]. AIC and BIC are utilised for model selection by balancing model fit and complexity, hence identifying the model that generalises best, namely the one that most accurately predicts behaviour on unseen data.\u003c/p\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003ePredictive Performance Metrics\u003c/h2\u003e \u003cdiv id=\"Sec12\" class=\"Section3\"\u003e \u003ch2\u003eMean Absolute Error (MAE)\u003c/h2\u003e \u003cp\u003eMAE quantifies the average size of errors in a series of forecasts, disregarding their direction (i.e., excluding overestimation or underestimation). [10]. It\u0026rsquo;s straightforward and interpretable.\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e\n$$\\:MAE=\\frac{1}{n}\\sum\\:_{t=1}^{n}|{y}_{t}-{\\widehat{y}}_{t}|,$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{t}\\)\u003c/span\u003e\u003c/span\u003e represents the true value, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{y}}_{t}\\)\u003c/span\u003e\u003c/span\u003e represents the anticipated value, whereas \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:n\\)\u003c/span\u003e\u003c/span\u003e denotes the quantity of observations.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003eRoot Mean Square Error (RMSE)\u003c/h2\u003e \u003cp\u003eRMSE quantifies the average magnitude of errors, assigning greater weight to larger discrepancies [10]. It exhibits greater sensitivity to outliers than MAE and is frequently employed when substantial errors are very unwelcome.\u003cdiv id=\"Eque\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Eque\" name=\"EquationSource\"\u003e\n$$\\:RMSE=\\sqrt{\\frac{1}{n}\\sum\\:_{t=1}^{n}{({y}_{t}-{\\widehat{y}}_{t})}^{2}}.$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003eMean Absolute Percentage Error (MAPE)\u003c/h2\u003e \u003cp\u003eMAPE quantifies the prediction error as a percentage of the actual value [10]. It\u0026rsquo;s often used in forecasting because it\u0026rsquo;s easy to interpret, but it can be biased if actual values are near zero.\u003cdiv id=\"Equf\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equf\" name=\"EquationSource\"\u003e\n$$\\:MAPE=\\frac{100}{n}\\sum\\:_{t=1}^{n}\\left|\\frac{{y}_{t}-{\\widehat{y}}_{t}}{{y}_{t}}\\right|$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003eResidual Analysis\u003c/h2\u003e \u003cdiv id=\"Sec16\" class=\"Section3\"\u003e \u003ch2\u003eLjung-Box test\u003c/h2\u003e \u003cp\u003eWhen building time series models, residual analysis is an important part to perform to test the assumptions and validity\u0026ensp;of the model [6, 23, 24]. This\u0026ensp;is done by checking residuals (the errors of predicted values) [25]. The most common\u0026ensp;diagnostic tests to assess residuals is Jung-Box. Jung-Box\u0026ensp;test to check for autocorrelation in residuals If residuals are correlated, that indicates failure of the model to capture\u0026ensp;all the temporal dependencies in the dataset [6].\u003c/p\u003e \u003cp\u003e \u003cstrong\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{H}_{0}\\)\u003c/span\u003e\u003c/span\u003e\u003c/strong\u003e \u003cp\u003eResiduals exhibit independence (absence of autocorrelation).\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{H}_{1}\\)\u003c/span\u003e\u003c/span\u003e\u003c/strong\u003e \u003cp\u003eThe residuals exhibit autocorrelation.\u003c/p\u003e \u003c/p\u003e \u003cp\u003eThe Ljung-Box test returns a p-value which is compared with a significance level (most\u0026ensp;commonly, 0.05) [6]. If the p-value exceeds 0.05, we are unable to reject \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{H}_{0}\\)\u003c/span\u003e\u003c/span\u003e: the residuals are not auto-correlated.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"Results","content":"\u003cp\u003eThe figure (1) shows the trend of under-five mortality in Kenya\u0026ensp;from 1995 onwards. Starting at around 109.5 deaths per 1,000\u0026ensp;live births in the early 1995, the rate continuously declined in the following decades, indicative of significant gains in child health outcomes. This downward trend is indicative of the associated\u0026ensp;benefits of improved healthcare access, increased immunisation coverage, better maternal care, and public health measures for preventable childhood illness. The continuous downward trajectory of the decline\u0026ensp;implies gradual progress without any significant underlying challenges, making Kenya a country that has made substantial progress in lowering rates of child mortality.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows Stationarity Test, Model Selection Metrics, and Model Performance Metrics for three models considered. Time series models apply to the mortality rates for under-fives (UFMR) in Kenya\u0026ensp;provide insight into trends and the chance of attaining that SDG 3.2 target: by 2030 The stationarity of the UFMR time series was tested with the Augmented\u0026ensp;Dickey-Fuller (ADF) test, which gave a test statistic of \u0026minus;\u0026thinsp;3.76 and p-value of 0.0033. This indicates that the time series is stationary, implies data, mean, variance, and autocorrelation structure do not change\u0026ensp;over time. Trusted time series models are based on the fundamental assumption of\u0026ensp;stationarity, which ensures that the underlying statistical properties remain unchanged and that predictions are based on an underlying uniformity in the data. This research article looks at how well three different models ARIMA, ARFIMA, and a hybrid of ARIMA and ARFIMA can predict the death rates of children under five. The optimal ARIMA model identified was (2, 1, 1), with an AIC value of 1345.21 and an RMSE of 1.98. This means that the ARIMA model fitted the trends\u0026ensp;in the data best. In contrast, the ARFIMA with parameters\u0026ensp;(1, 0.4, 1) yielded a poorer fit to the data (RMSE is 2.85, AIC is 1360.45). The hybrid model, which combined ARIMA and ARFIMA, outperformed ARFIMA on an AIC of 1350.33\u0026ensp;and RMSE of 2.35 but still fell short of the ARIMA results. The AIC and RMSE values\u0026ensp;indicated that the ARIMA model performed the best for predicting under-five mortality rates in Kenya.\u003c/p\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\u003eStationarity Test, Model Selection Metrics, and Model Performance Metrics.\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=\"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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eStationarity Test\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eADF statistics\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003efinal p-value\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStationary\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-3,76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0033\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e\u003cb\u003eModel Selection Metrics\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBest (p, d, q)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAIC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eARIMA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(2,1,1)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1345.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eARFIMA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(1,0.4,1)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1360.45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.85\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHybrid\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e(2,1,1) \u0026amp; (1,0.4,1)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1350.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.35\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e\u003cb\u003eModel Performance Metrics\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMAPE (%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eR\u0026sup2;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eARIMA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.92\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eARFIMA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.87\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHybrid\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.89\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e\u003cb\u003eResidual Analysis\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eP-value\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDecision\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0033\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNot significant\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e\u003cp\u003eWe then evaluated the performance of our models, applying RMSE, MAPE (Mean Absolute Percentage Error), MAE (Mean Absolute Error), and R\u0026sup2; (Coefficient of Determination) as\u0026ensp;metrics. The result\u0026ensp;showed that the ARIMA which achieves best performance RMSE of 2.34, MAPE of 3.21%, MAE of 1.98, R\u0026sup2; of 0.92. This high R-squared number indicates that ARIMA provides a model\u0026ensp;for 92% of the data variability in under-five mortality which reflects a good fit to the data. The ARFIMA model had the worst performance with an RMSE of 3.12, MAPE of 4.56%, and\u0026ensp;R\u0026sup2; of 0.87; however, the Hybrid model had similar performance to ARFIMA (RMSE\u0026thinsp;=\u0026thinsp;2.85, MAPE\u0026thinsp;=\u0026thinsp;3.78%, and R\u0026sup2; = 0.89).\u003c/p\u003e\n\u003cp\u003eThe ARIMA model was also validated with its residual\u0026ensp;analysis using Ljung-Box test. The p-value for the residuals was 0.0033, which indicated that residuals were significant so that the model\u0026apos;s assumptions which stated that residuals must possess properties of white noise\u0026ensp;were satisfied. Based on this finding, the ARIMA model was confirmed to be reliable as a predictive model for under-five death rates in Kenya.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eThis article investigates progress on under-five mortality rates\u0026ensp;(UFMR) in Kenya by estimating time-series models (such as ARIMA, ARFIMA, and Hybrid) to predict trends and determine the probability of meeting the SDG 3.2 target of 25 deaths per 1000 live births by 2030. The ARIMA model output show a declining trend in under-five mortality, but the forecast indicates that the SDG target may not be\u0026ensp;reached in Kenya. This finding is in line with global trends emphasized by Granger and Newbold [9] who described the efficiency of time series in forecasting exact economic and health outcomes but also highlight the uncertainties which are arrogant\u0026ensp;projections. Montgomery et al. [10] underscore the importance of utilizing robust time series models, such as ARIMA, for forecasting trends in health indicators, including morbidity and mortality rates, based on the premise that future trends are unlikely to deviate from historical patterns.\u003c/p\u003e \u003cp\u003eConsistent with Sachs et al. [3] achieving the targets of SDG\u0026ensp;3 will take continued cross-sectoral action, our data suggests that while Kenya made great advances in reducing the under-five mortality ratio, achieving the SDG 3.2 target will likely require additional action. And the observed and projected death\u0026ensp;rates are plateauing, as Kenya approaches but don\u0026rsquo;t quite reach target. As noted by Moyer and Hedden [4], investment will be needed in health infrastructure, education and socio-economic development in countries such as Kenya\u0026ensp;if SDG 3.2 target is to be achieved by 2030, else the achievement will be a tall order. The hybrid model which is employed in this study contains both the ARIMA and ARFIMA parts, and hence more\u0026ensp;sophisticated modelling can explain further issues such as the effect of long-memory processes [5] on mortality.\u003c/p\u003e \u003cp\u003eMoreover, Yovo [2] discusses the struggles that resource-blighted settings will face in meeting sustainable development goal (SDG) 3.2 targets, thus alluding to restricted healthcare\u0026ensp;resources and infrastructure that correspond with the results predicted by our study. While the model predicted this to be not only within target threshold UFMR is well below and well above the threshold it emphasizes the point of the need to focus interventions (through targeted\u0026ensp;health policy) and moreover, more importantly, specifically rural and lower socioeconomic areas. Das et al. [1] calling for\u0026ensp;integrated approaches to access and equity in health as a prerequisite for continued progress towards SDG 3, especially in the context of Southeast Asia.\u003c/p\u003e \u003cp\u003eThese results are consistent with the general narrative of health\u0026ensp;issues for Africa, which prompted Golding et al. [26] as highlighted\u0026ensp;in their mapping of under-five mortality across the continent. Kenya is making strides but not on track to meet the SDG\u0026ensp;target, according to baseline analysis of under-five and newborn mortality by Golding et al. [26]. This addresses a large problem in multiple sub-Saharan African countries and shows\u0026ensp;that targeted cross-sectoral initiatives are necessary on the way to achieve SDG 3.2.\u003c/p\u003e \u003cp\u003eDependence of the forecasting\u0026ensp;model on historical data (1995\u0026ndash;2022) may underperform if future mortality trends will be influenced by unanticipated external factors like economic or health crises like the impact of epidemics of the like COVID-19 pandemic. Fischer and Carow [27] highlighted that global health initiatives need to address additional threats and challenges to sustain progress, and this restriction is consistent\u0026ensp;with that assertion. The next models might comprise an additional dataset, inclusive of panel data and external factors, for instance, health regulations, economic conditions, and interventions,\u0026ensp;as reflected in the work of Saleh et al. [7] support\u0026ensp;for predictive models that leverage diverse datasets to improve forecasting accuracy\u003c/p\u003e "},{"header":"Conclusion and Recommendations","content":"\u003cdiv id=\"Sec19\" class=\"Section2\"\u003e\n \u003cp\u003eThis paper highlights on Kenya\u0026apos;s progress towards the SDG 3.2 goal of reducing under-five mortality to 25 deaths per 1,000\u0026ensp;live births by the year 2030. The ARIMA model, which fit the historical\u0026ensp;data best, indicates that under-five mortality rates have been decreasing steadily from 1995 to 2022, but projections suggest that Kenya is unlikely to meet the SDG target by 2030 without further interventions. This highlights the immediate need for more focus on protecting\u0026ensp;the achievements seen so far, especially in vulnerable populations that still have a higher risk of mortality.\u003c/p\u003e\n \u003cp\u003eAttainment of SDG 3.2 targets by Kenya will need to ensure effective health systems in maternal and child healthcare services that are critical to the reduction\u0026ensp;of avoidable deaths. Even as we see positive trends with the continuing decline in preventable mortality, they indicate the need for faster, wider momentum and a linkage with\u0026ensp;the access to quality health-care services, reduction of adverse socio-economic determinants and adoption of nutrition interventions. It also highlights which groups at risk such as women, people living in rural communities, and those in low-income households\u0026ensp;will require tailored interventions to achieve the mortality target of the Sustainable Development Goals.\u003c/p\u003e\n \u003cp\u003ePanel data\u0026ensp;from more countries in sub-Saharan Africa will allow for more comprehensive analysis and comparisons among health care systems and health interventions in the region. Additionally, for better prediction accuracy more studies should be conducted\u0026ensp;regarding inclusion of external factors like policy changes, economic development, and health expenditure towards infrastructural predictive modeling. This could yield better forecasts with advanced methodology, including machine learning techniques that account for non-linear correlations\u0026ensp;and recognize elaborate patterns within the data. Expanding the research scope can help policymakers to better understand\u0026ensp;the multi-faceted drivers of under-five mortality and to develop solutions that are more likely to achieve SDG 3.2 by 2030.\u003c/p\u003e\n\u003c/div\u003e\n"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eApproval of ethics and consent for participation.\u003c/strong\u003e\u0026nbsp;\u003cbr\u003e\u0026nbsp;Irrelevant.\u0026nbsp;\u003cbr\u003e\u003cstrong\u003eFunding sources\u003c/strong\u003e\u0026nbsp;\u003cbr\u003e\u0026nbsp;This study received no money from any sources or employers.\u0026nbsp;\u003cbr\u003e\u003cstrong\u003eContributions of the author\u003c/strong\u003e\u0026nbsp;\u003cbr\u003e\u0026nbsp;WJD: The author designed the study, sourced data from the World Bank website, conducted data extraction and processing, performed data analysis and interpretation, drafted the initial paper, and composed the final manuscript. SFM and HGM evaluated and provided feedback on the entire paper.\u0026nbsp;\u003cbr\u003e\u003cstrong\u003eConsent\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot Applicable.\u0026nbsp;\u003cbr\u003e\u003cstrong\u003eStatement of Conflicting Interests\u003c/strong\u003e\u0026nbsp;\u003cbr\u003e\u0026nbsp;The author(s) disclosed no potential conflicts of interest regarding the research, writing, and/or publication of this paper.\u0026nbsp;\u003cbr\u003e\u003cstrong\u003eRecognition\u0026nbsp;\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;The author expresses profound gratitude to the World Bank for the collection and provision of data, as well as to the University of KwaZulu-Natal and North-West University for their support.\u003c/p\u003e\n"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eDas T, Holland P, Ahmed M, Husain L, Ahmed M, Husain L. Sustainable development goal 3: good health and well-being. In South-East Asia Eye Health: Systems, Practices, and Challenges 2021 Aug 19 (pp. 61-78). Singapore: Springer Singapore.\u003c/li\u003e\n\u003cli\u003eYovo E. Challenges on the road to achieving the SDG 3.2 targets in resource-limited settings. The Lancet Global Health. 2022 Feb 1;10(2):e157-8.\u003c/li\u003e\n\u003cli\u003eSachs J, Kroll C, Lafortune G, Fuller G, Woelm F. Sustainable development report 2022. Cambridge University Press; 2022.\u003c/li\u003e\n\u003cli\u003eMoyer JD, Hedden S. Are we on the right path to achieve sustainable development goals?. World Development. 2020 Mar 1;127:104749.\u003c/li\u003e\n\u003cli\u003eShumway RH, Stoffer DS, Shumway RH, Stoffer DS. ARIMA models. Time series analysis and its applications: with R examples. 2017:75-163.\u003c/li\u003e\n\u003cli\u003eMwijalilege SA, Kadigi ML, Kibiki C. Comparing ARFIMA and ARIMA Models in Forecasting under Five Mortality Rate in Tanzania. Asian Journal of Probability and Statistics. 2025 Jan 15;27(1):107-21.\u003c/li\u003e\n\u003cli\u003eSaleh MH, Alkhawaldeh RS, Jaber JJ. A predictive modeling for health expenditure using neural networks strategies. Journal of Open Innovation: Technology, Market, and Complexity. 2023 Sep 1;9(3):100132.\u003c/li\u003e\n\u003cli\u003eDiggle P, Giorgi E. Time Series: A Biostatistical Introduction: A Biostatistical Introduction. Oxford University Press; 2025 Feb 25.\u003c/li\u003e\n\u003cli\u003eGranger CW, Newbold P. Forecasting economic time series. Academic press; 2014 May 10.\u003c/li\u003e\n\u003cli\u003eMontgomery DC, Jennings CL, Kulahci M. Introduction to time series analysis and forecasting. John Wiley \u0026amp; Sons; 2015 Apr 27.\u003c/li\u003e\n\u003cli\u003eHorv\u0026aacute;th L, Kokoszka P, Rice G. Testing stationarity of functional time series. Journal of Econometrics. 2014 Mar 1;179(1):66-82.\u003c/li\u003e\n\u003cli\u003eJalil A, Rao NH. Time series analysis (stationarity, cointegration, and causality). InEnvironmental kuznets curve (EKC) 2019 Jan 1 (pp. 85-99). Academic Press.\u003c/li\u003e\n\u003cli\u003eHuang C, Petukhina A. ARMA and ARIMA Modeling and Forecasting. In Applied Time Series Analysis and Forecasting with Python 2022 Oct 20 (pp. 107-142). Cham: Springer International Publishing.\u003c/li\u003e\n\u003cli\u003eGr\u0026eacute;goire G. An overview of this book. Statistics for Astrophysics. Time Series Analysis. 2022:9-33.\u003c/li\u003e\n\u003cli\u003eMonge M, Infante J. A fractional ARIMA (ARFIMA) model in the analysis of historical crude oil prices. Energy Research Letters. 2023 Jan 31;4(1).\u003c/li\u003e\n\u003cli\u003eKartikasari P, Yasin H, Di Asih IM. ARFIMA model for short term forecasting of new death cases COVID-19. InE3S Web of Conferences 2020 (Vol. 202, p. 13007). EDP Sciences.\u003c/li\u003e\n\u003cli\u003eKumar H, Patil SB. 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Academic Press; 2014 May 10. \u003c/li\u003e\n\u003cli\u003eGolding N, Burstein R, Longbottom J, Browne AJ, Fullman N, Osgood-Zimmerman A, Earl L, Bhatt S, Cameron E, Casey DC, Dwyer-Lindgren L. Mapping under-5 and neonatal mortality in Africa, 2000\u0026ndash;15: a baseline analysis for the Sustainable Development Goals. The Lancet. 2017 Nov 11;390(10108):2171-82. \u003c/li\u003e\n\u003cli\u003eFischer F, Carow F. Impact of public health and sustainability of global health action for achieving SDG 3. Transitioning to good health and well-being. 2022 Aug 23:111-32.\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":true,"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":"Under-five mortality, Sustainable Development Goal 3, Time series analysis, ARIMA, Hybrid models, Kenya","lastPublishedDoi":"10.21203/rs.3.rs-6602153/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6602153/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eBackground\u003c/h2\u003e \u003cp\u003eSustainable Development Goal (SDG) 3.2 is to decrease the under-five mortality rate to under 25 per 1,000 live births by 2030. This is a critical objective for enhancing child health, especially in sub-Saharan Africa, where mortality rates persist at elevated levels.\u003c/p\u003e\u003ch2\u003eObjective\u003c/h2\u003e \u003cp\u003eThis article evaluate progress made in Kenya towards Sustainable Development\u0026ensp;Goal (SDG) 3.2 (by 2030). Further assess historical trends in under-five mortality, project future mortality rates and assess the feasibility of achieving the Sustainable\u0026ensp;Development Goal target.\u003c/p\u003e\u003ch2\u003eMethod\u003c/h2\u003e \u003cp\u003eThis article utilises panel data from 1995\u0026ndash;2022 and three time series models which includes ARIMA, ARFIMA, and a Hybrid model. The most effective model was determined to be\u0026ensp;an ARIMA (2,1,1) based on the lowest AIC, RMSE (2.34) and MAPE (3.21%), i.e., it was the best fit model through comparison with the others. The MAE was 1.98, support\u0026ensp;for the model's correction. These metrics were used to evaluate model predicative accuracy and their\u0026ensp;usefulness in predicting future under-five mortality.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e \u003cp\u003eThe paper presents evidence of a downward trend in under-five mortality in Kenya, which the ARIMA model forecasts toward improvements in the\u0026ensp;coming years. The forecast suggests Kenya is unlikely to meet the SDG 3.2\u0026ensp;goal, since the predicted articulation of the mortality rate is projected to plateau above the targeted level by 2030. This implies that\u0026ensp;more actions need to be put in place to achieve the goal.\u003c/p\u003e\u003ch2\u003eConclusion\u003c/h2\u003e \u003cp\u003eKenya has made strides in reducing under-five mortality, but it will fall short of its SDG 3.2 target by 2030 without further\u0026ensp;investment in interventions. Emphasis on healthcare provision, nutrition as well\u0026ensp;as addressing socio-economic differences are required to achieve the goal.\u003c/p\u003e","manuscriptTitle":"Tracking Progress Towards Sustainable Development Goal 3.2 Target in Kenya: A Time Series Analysis","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-05-19 07:56:37","doi":"10.21203/rs.3.rs-6602153/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":"2c0afb60-c91b-4f66-bed7-cf945c7e945a","owner":[],"postedDate":"May 19th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-07-19T07:23:44+00:00","versionOfRecord":[],"versionCreatedAt":"2025-05-19 07:56:37","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6602153","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6602153","identity":"rs-6602153","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}