Wavelet-Driven LSTM Modelling for Exchange Rate Forecasting in BRICS Economies

Wavelet-Driven LSTM Modelling for Exchange Rate Forecasting in BRICS Economies | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Wavelet-Driven LSTM Modelling for Exchange Rate Forecasting in BRICS Economies Haseen Ahmed This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8199826/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 This study evaluates the predictive performance of Wavelet-LSTM models in forecasting exchange rates for BRICS currencies (INR, CNY, RUB, BLR, and ZAR). The data period studied is from March 2013 to February 2024. The analysis reveals significant variability in model performance, with the Chinese Yuan (CNY) exhibiting robust predictive accuracy, as indicated by low errors and high R² values on both training and test datasets. Conversely, the Indian Rupee (INR) and South African Rand (ZAR) show poor test set performance, highlighting overfitting and limited generalization capabilities. Moderate performance for the Russian Ruble (RUB) and Brazilian Real (BLR) suggests potential for improvement through fine-tuning. These findings underscore the need for strategies such as regularization, cross-validation, and enhanced data preprocessing to address overfitting and improve generalization. A tailored, currency-specific modelling approach is recommended to account for diverse exchange rate dynamics. Future research should explore advanced techniques, including ensemble learning, to enhance model robustness and applicability across varying economic contexts. JEL Classification - C45, F31, C53, O57 Macroeconomics Neural Networks Forex Forecasting BRICS Wavelet Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction The prediction of exchange rates in BRICS countries (Brazil, Russia, India, China, and South Africa) holds significant importance in the current global geopolitical environment, given their critical roles in global trade, investment flows, and economic alliances. The geopolitical risk is key determinant of variations in financial markets and investment related decisions (Pastor and Veronesi, 2013). BRICS countries are recipient of global investment from the major countries like Japan, USA, and Germany (Sui and Sun, 2016 ), are affected by the investment flows from abroad, and exchange rate regime followed. Exchange rate fluctuations directly impact trade balances, affecting export competitiveness and import costs. In a world where BRICS countries are deepening their trade ties and economic cooperation, predicting exchange rates allows businesses to manage risks and optimize profits. BRICS group consists 42 percent of world population, 23 per cent of GDP, 30 per cent of territory, and 18 per cent of trade (Salisu et al., 2022 a ). Additionally, the geopolitical tensions, such as Russia’s involvement in the Ukraine war and rising U.S.-China rivalries, have added uncertainty to exchange rate movements. Accurate predictions help governments and businesses mitigate these risks, maintaining stability in trade and pricing. Amid the ongoing internationalisation of BRICS currencies, de-dollarization and discussions around a potential common BRICS currency, accurate forecasting can strengthen the feasibility of its introduction (Coquidé et al. 2023 ; Kondratov, 2021 ; Das and Roy, 2023 ; Ahmed et al., 2025 ; Atif et al., 2022 ; Ahmed, 2025 c). Moreover, exchange rates influence inflation by affecting the costs of imported goods, which is particularly sensitive for BRICS nations like Brazil and South Africa. Predicting exchange rate trends enables central banks to craft monetary policies that control inflation and stabilize economies. BRICS members are also exploring currency cooperation, including discussions on a common currency, making exchange rate forecasts vital for assessing the feasibility and impact of such initiatives. Investors rely on these predictions to assess the risks and returns of foreign direct investment (FDI) and portfolio investments. Currency volatility can deter investment or cause capital flight, making stable forecasts essential for attracting and retaining capital inflows. For resource-dependent BRICS countries, such as Russia, Brazil, and South Africa, exchange rate forecasts are also critical for predicting commodity prices and revenues, especially in response to global demand shifts. Governments and central banks rely heavily on exchange rate predictions for policy formulation and economic planning, influencing interest rates, trade tariffs, and fiscal strategies. As BRICS nations seek to position themselves in a more multipolar world, the ability to accurately predict exchange rates has become both an economic and geopolitical necessity (Salisu et al., 2021 b ). Traditional econometric methods, such as ARIMA, VAR, and GARCH, have been widely used to forecast exchange rates. However, these methods face several challenges such as linear assumption, as the movement of forex rates is complex, and nonlinear due to factors such as interest rates, inflation, geopolitical events, and market sentiment. The traditional model flexibility with big data is limited, and often fail to account for external shocks (Ramos-Pérez et al. 2019 ; Liu, 2019 ; Pradeepkumar and Ravi, 2017 ). The assumption of stationarity, that statistical properties are constant over the time, is also limitation of traditional models, along with the model specification such as lag length, autocorrelation etc. In recent, the literature around time series forecasting using Artificial Intelligence (AI) has grown significantly. Machine learning ML, and DL models, such as ANNs, random forests, and SVMs, offer several advantages over traditional econometric methods in predicting exchange rates. The ML models excel at capturing complex and nonlinear linkages and can detect hidden patterns in data (Srivastava et al. 2023 ; Rubio et al 2023 ; Kamalov et al. 2022 ). Further, the machine learning models can process the large datasets, incorporating multiple factors. The ML and DL based models can also adapt to non-stationary data. The RNNs or LSTM technique are efficient in handling the time series with changing patterns. The AI based models can be trained on high-frequency data, enhancing the ability to handle the external shocks. Further, the Automatic feature selection, robustness and flexibility, and overall improved forecast accuracy. Due to this, the ML techniques are increasingly becoming a preferred approach for exchange rate forecasting in the evolving global financial environment (Zhang et al. 2024 ). A promising approach to address this complexity is the utilization of Wavelet-LSTM networks. This hybrid model integrates the advantages of wavelet analysis, which facilitates the decomposition of time series data into distinct frequency components, with the robust sequential learning capabilities of LSTM neural networks (Tamilselvi et al. 2024 ; Chen et al. 2019 ). By employing this methodology, researchers can effectively capture both long-term trends and short-term fluctuations in BRICS forex rates, potentially enhancing forecast accuracy. The wavelet decomposition process contributes to the management of non-stationary data and the reduction of noise, while the LSTM network demonstrates proficiency in learning intricate temporal dependencies. This approach may prove particularly valuable for policymakers, investors, and financial institutions operating within BRICS countries, as it has the potential to yield more reliable predictions of forex rate movements in these volatile markets. Forecasting foreign exchange (forex) rates in BRICS economies presents a significant challenge due to the dynamic nature of these emerging markets. The complexity of these economies, characterized by rapid growth, evolving financial systems, and susceptibility to global economic shifts, necessitates sophisticated forecasting techniques. A promising approach to address this complexity is the utilization of Wavelet LSTM networks. This hybrid model integrates the advantages of wavelet analysis, which facilitates the decomposition of time series data into distinct frequency components, with the robust sequential learning capabilities of LSTM neural networks. This methodology captures both long-term trends and short-term fluctuations in BRICS forex rates can be captured, potentially enhancing forecast accuracy. The wavelet decomposition process contributes to the management of non-stationary data and the reduction of noise, which are common challenges in forex rate analysis. This step allows for a more nuanced examination of the underlying patterns in the time series data, separating high-frequency fluctuations from low-frequency trends. Such decomposition can reveal hidden structures within the data that might be obscured in traditional time series analysis methods. The LSTM network, a specialized form of recurrent neural network, demonstrates proficiency in learning intricate temporal dependencies. This capability is particularly valuable in forex rate prediction, where complex interactions between various economic factors, geopolitical events, and market sentiments influence exchange rates over different time horizons. LSTM networks can effectively capture and remember relevant information over extended periods, making them well-suited for identifying long-term dependencies in forex rate movements. The combination of wavelet analysis and LSTM networks in this hybrid approach offers several advantages. Firstly, it allows for the simultaneous consideration of multiple time scales, from short-term fluctuations to long-term trends, providing a more comprehensive view of forex rate dynamics. Secondly, the noise reduction achieved through wavelet decomposition can lead to more stable and reliable input features for the LSTM network, potentially improving the overall predictive performance. This approach is valuable particularly, for policymakers, investors, and financial institutions operating within BRICS countries, as it has the potential to yield more reliable predictions of forex rate movements in these volatile markets. Policymakers can utilize these forecasts to inform monetary policy decisions and manage currency stability. Investors and traders can leverage the predictions to optimize their portfolio strategies and manage risk exposure in BRICS currencies. Financial institutions can enhance their risk management practices and improve their foreign exchange operations based on more accurate forecasts. Moreover, the application of Wavelet LSTM networks to BRICS forex rate forecasting opens up avenues for further research and development in the field of financial time series analysis. Researchers can explore variations of this hybrid model, such as incorporating additional economic indicators or experimenting with different wavelet transformation techniques to further refine the forecasting accuracy. The success of this approach in BRICS economies could also pave the way for its application in other emerging markets or even developed economies, contributing to the broader field of economic forecasting and financial modelling. Literature Review The use of machine learning and deep learning has grown significantly in the prediction of the time series variables(Ahmed, 2025 a, 2025 b, 2025 d, 2025 e). The use of ML and DL has advantages of accuracy and capturing the non-linearity and complexity of the time series variables, irrespective of the stationarity and normality, the necessary assumptions of the many traditional methods of forecasting. The review study by, Junior et al. (2023) provides, comprehensive background of the previous research in the forex market forecasting, whereas the Liu and Wang ( 2024 ), reviewed ML and DL models used in the time series prediction. The selection of model and evaluation is crucial in accurate prediction. To probe this question, Junior et al. (2023) reviewed the literature of forex forecasting methodologies. In reviewing of 60 studies from 2010 to 2021, authors found use of LSTM and ANN models to be most commonly used algorithm of machine learning. Further, authors found that MSE, RMSE, MAE, and MAPE were the most commonly used evaluation metrics. Authors concluded that there is significant scope of research in the exchange rate prediction. As per Fletcher ( 2012 ), the SVM, Relevance Vector Machine (RVM) and Neural Network shows improved results when exogenous variables, affecting the basket of forex returns are included. Panda et al. ( 2020 ) reviewed the advance exchange rate prediction of studies from 2000 to 2019. The author found the use of different models such as ANN, FLANN, HMM, SVM, and AR models. Islam et al. ( 2020 ) examined the studies which have studied the advancements in forex prediction. Based on the analysis of 39 studies from select publishers, author found the use of neural networks, GRU and LSTM to be most prevalent in the forecasting of exchange rates. In their review, Sezer et al. ( 2020 ) indicated increased use of DL methods in time series forecasting. Berradi et al. (2020) favoured the deep learning techniques over the traditional ones in the forecasting of time series. The study further found that RNNs are mostly used model in the predictions. Ryll and Siedens (2019) evaluated the machine learning models from 150 research papers, and found them to be outperforming the traditional models. Further, among the findings, the RNN models perform better than the feed forward neural network as well as SVM. The findings hinted at the temporal effect in prediction across the assets and location, and can be utilised in forecasting of time series. Henriques et al. (2019) recognised the difficulty in forecasting the financial time series due to chaotic, non-linear and dynamic nature of them. Further in the findings of bibliometric analysis, SVM and neural networks are the dominantly used ML models, and data is mostly used from north American markets. Authors suggested the relevancy of the research field, and required focus on the data of emerging markets. Abedin et al. ( 2021 ) proposed a model by combining the bagging ridge regression and Bi-LSTM model to predict the forex rate of 21 currencies before the Covid and after the Covid. Further, the authors compared the models with the traditional models such as SVM, Decision Tree, random forest as well as DL methods of LSTM and Bi-LSTM. The proposed model was found to be more accurate, however, the accuracy varied before and during the pandemic. Dautel et al. ( 2020 ) compared the LSTM and GRU with the traditional recurrent network architecture and feedforward network in directional forecasting. The authors found the DL methods to be suitable in prediction, but also pointed out the difficulty in tuning and implementing the architectures. Rabbi et al. ( 2022 ) forecasted the currencies of 22 countries by using the various ML and DL techniques. Out of the SVR, and RVR, and LSTM. The LSTM is found to be the more accurate as compared to the others. Datta et al. ( 2021 ) proposed different ML and DL models in prediction of 22 currencies. The study employed the lasso regression, decision tree, ridge regression, and the Bi-LSTM in prediction, and found the Bi-LSTM to be better performing as compared to the other models. The MAE, MSE, RMSE, and MAPE were used to evaluate the model accuracy. Ince and Trafalis ( 2006 ) proposed forecasting model combining the parametric and non-parametric test such as ARIMA and VAR, with the SVR and ANN. The study found the SVR technique to be accurate in performance. Wang et al. ( 2022 ) proposed the CNN-TLSTM model in prediction of Canadian dollar. The CNN model selects the features whereas the TLSTM does the prediction of time series. In comparison of MLP, CNN, RNN, LSTM and CNN-LSTM, the CNN-LSTM model is found to be better predictor of the Chinese Yuan forex rate. Wang and Chen ( 2021 ) combine the two-stage feature extraction model and Adaboost based reinforcement ensemble learning framework. The resultant deep RNN, is found to be a better in accuracy. Islam and Hossain ( 2021 ) combined the LSTM and GRU to predict the four commonly used currencies, EUR, GBP, CAD, and CHF. The author also compared the model with the standalone LSTM and GRU. on the basis of MSE, RMSE, MAE, and R-Squared, the study found the combined LSTM-GRU model to be best performing. On the basis of the analysis of above, it can be noticed that literature has been in the favour of deep learning in forecasting of the time series data. Further, it can be observed that, the use of combination of traditional and deep learning models is lacking in time series forecasting. The wavelet LSTM model is widely used in forecasting of various type of variables, such as wind power, fault in power grids, solar irradiance, electricity price prediction, stock market prediction, fault detection in rotating machinery, air quality, electricity consumption (Liu et al., 2019 ; Branco et al., 2022 ; Wang et al., 2018 ; Chang et al., 2019 ; Jalayer et al., 2021 ; Zeng et al., 2022 ; Chi, 2022 ). However, the use wavelet LSTM in forex rate forecasting has not been observed in the literature. To the best of authors knowledge, no study has applied the combined approach of Wavelet-LSTM in forex rate prediction. This study probes the predictive accuracy of this ensemble model this paper. This study aims to investigate the predictive accuracy of a Wavelet Transformed LSTM model in forecasting forex rates for the BRICS countries. By combining the signal processing capabilities of wavelets with the powerful temporal learning abilities of LSTM, this novel approach may provide valuable insights and improved forecasting performance compared to existing methods. Methods and Materials Data The data consists the crude oil prices and forex rate of five BRICS countries. The variables are OIL – Brent crude oil prices, INR-Indian Rupee, CNY- Chinese Yuan, RUBLE- Russian Ruble, and ZARSA denotes South African Rand. Table 1 – Descriptive Statistics OIL INR CNY RUBLE BLR ZARSA Mean 72.075 69.629 6.6150 62.636 3.9085 14.152 Std. Error 0.4392 0.1372 0.0064 0.2997 0.0207 0.0480 Median 68.695 68.660 6.6061 64.092 3.8211 14.261 Mode 70.710 64.860 7.1942 32.985 5.1706 14.485 Std. Dev 23.688 7.3999 0.3452 16.164 1.1214 2.5887 Sam. Var 561.14 54.758 0.1192 261.28 1.2575 6.7015 Kurtosis -0.7537 -0.6437 -1.1339 0.4219 -1.2346 -0.5920 Skewness 0.2884 0.1669 0.1397 -0.2314 -0.0354 0.0014 Range 124.06 30.391 1.3063 113.13 3.9445 11.347 Minimum 9.1200 53.035 6.0412 29.863 1.9447 8.4580 Maximum 133.18 83.426 7.3475 143.00 5.8892 19.805 Source – Author’s Work The descriptive statistics for the five BRICS currencies (INR, CNY, RUBLE, BLR, and ZARSA) and oil prices reveal important insights into their central tendencies, dispersion, and distribution shapes. The mean values show that oil prices averaged $ 72.08, while the Indian Rupee (INR) averaged 69.63, the Chinese Yuan (CNY) 6.62, the Russian Ruble (RUBLE) 62.64, the Brazilian Real (BLR) 3.91, and the South African Rand (ZARSA) 14.15 per US Dollar. Among these currencies, the CNY exhibited the least fluctuation around its mean with a small standard error of 0.0064, indicating its relative stability, while the RUBLE had the largest standard error of 0.2998, signifying greater variability in its average exchange rate. Standard deviation (a measure of dispersion) and variance (the square of standard deviation) further highlight the variability of these currencies. The RUBLE shows the highest standard deviation (16.16) and variance (261.29), confirming its status as the most volatile currency in the group. In contrast, the CNY has the smallest standard deviation (0.345) and variance (0.119), underscoring its stability. The INR and ZARSA show moderate variability, with standard deviations of 7.40 and 2.59, respectively. When examining kurtosis, the most currencies, including the INR, CNY, BLR, and ZARSA, have negative kurtosis values, indicating flatter distributions with fewer extreme values. The RUBLE, with a slightly positive kurtosis (0.42), indicates a higher likelihood of extreme values or outliers in its data. Skewness, which measures asymmetry in the data, is generally close to zero for most currencies, with the INR, CNY, and ZARSA showing slightly positive skewness, suggesting a nearly symmetric distribution but with a slight tilt towards higher values. On the other hand, the RUBLE and BLR exhibit slight negative skewness, meaning their distributions have more frequent lower values. Wavelet – LSTM Wavelet Long Short-Term Memory (Wavelet LSTM) is a hybrid model that combines wavelet transform techniques with Long Short-Term Memory (LSTM) neural networks to enhance time-series forecasting. The wavelet transform decomposes the original time-series data into different frequency components, allowing the model to focus on both short-term fluctuations and long-term trends separately. By capturing both high and low-frequency information, Wavelet LSTM improves the model's ability to predict complex time-series patterns more effectively than traditional LSTM models, which may struggle with multi-scale data. The process typically involves applying the discrete wavelet transform (DWT) to decompose the input time-series \(\:x\left(t\right)\) into approximation (A) and detail (D) coefficients at different levels of decomposition. These components are then fed into separate LSTM models, which are specialized in learning temporal dependencies from each frequency band. The outputs of the LSTM models are then aggregated, often by reconstructing the signal through an inverse wavelet transform (IWT), to provide the final forecast. Mathematically, the wavelet decomposition of the time-series \(\:x\left(t\right)\) can be expressed as: $$\:x\left(t\right)=A\left(t\right)+D\left(t\right)$$ 1 Where \(\:A\left(t\right)\) represents the low-frequency components (approximation), and \(\:D\left(t\right)\) represents the high-frequency components (details). These components are then processed individually through LSTM layers to predict future values: $$\:\widehat{y}\left(t\right)={LSTM}_{A}\left(A\left(t\right)\right)+{LSTM}_{D}\left(D\left(t\right)\right)$$ 2 Finally, the predicted components are combined to form the overall forecast. The Wavelet LSTM approach is particularly useful in scenarios with complex, noisy, or multi-scale data, such as financial markets, where different time frames may show distinct patterns. Evaluating models goes beyond simply checking their accuracy; it's about assessing their reliability in making predictions. The accuracy and reliability are crucial in making forecast. There are various metrics which evaluate the models, including MSE, RMSE, and R-squared. Various studies have used the MSE, RMSE, and R-Square for the evaluation of forecasting accuracy of the machine learning models (Alqahtani & Abdelhafez, 2023 ; Aziz et al., 2022 ; Chen, 2023 ; Kandil et al., 2023 ; Muganda & Kasamani, 2023 ; Nanthiya et al., 2023 ; Prakash & Singh, 2022 ; Wang et al., 2022 ; Ahmed and Kaur, 2025 ). In machine learning, MSE and RMSE gauge how accurate a model's predictions are by capturing the average difference among forecasted and observed values. MSE acts like a trainer during the learning process, guiding the model to minimize this error. It excels at penalizing the large mistakes because it penalizes huge differences more heavily. However, MSE is measured in squared units, different from the target variable's unit, making interpretation a bit complex. To address this, RMSE simply takes the root square of MSE, presenting the error in the same units as the target variable for easier understanding. Both metrics are popular for their focus on large errors but are also sensitive to outliers, so keep the target variable's unit in mind when evaluating the error values. The R squared focuses on the part of variance explained in the dependent variable by the model. It essentially quantifies how well the model fits the data, indicating the degree to which it can explain the target variable's variance. R-squared is an easy-to-understand measure of model fit, and varies from zero to one, where one signifies a perfect fit. While it's scale-independent, adding more predictors can artificially inflate R-squared. Importantly, R-squared about the model's predictive power; it simply helps us understand the proportion of variance explained by the factors considered in the model. Results and Findings The graph in Fig. 1 illustrates a comparison between the actual and predicted INR exchange rates of test data using a Wavelet-LSTM model. The data was split in ratio of 80:20. The test data predictions are based on the trained data by the used algorithm. The blue line represents the actual exchange rate, showing real-world fluctuations over time, marked by periods of sharp increases and decreases. In contrast, the orange line represents the model's predictions, which, while capturing the general trend, appear much smoother and show fewer sharp fluctuations than the actual data. From graph, it can be observed that is the underestimation of volatility by the Wavelet-LSTM model. Although the model successfully tracks the overall trend, it struggles to predict the more rapid and extreme changes in the exchange rate. The predicted line, while aligned with the overall direction of movement, fails to capture the sharp spikes or dips that are evident in the actual data. This suggests that the model captures long-term trends effectively but may need further refinement to accurately model short-term volatility. Overall, the Wavelet-LSTM model performs well in forecasting general trends but leaves room for improvement in handling rapid and complex fluctuations in exchange rates. The graph in Fig. 2 indicate the predicted and actual values of Chinese Yuan. The blue line represents the actual CNY exchange rate, showing its real fluctuations over time. In this case, the model appears to perform well, closely following the actual exchange rate movements with a good degree of accuracy. The model tracks trends and volatility, with the predicted line closely mirroring the peaks, troughs, and general direction of the actual data. While there are some minor discrepancies, particularly around the sharper changes in the exchange rate, the predicted values align well with the overall pattern of the actual exchange rate. This suggests that the Wavelet-LSTM model is effectively capturing both short-term fluctuations and long-term trends in the CNY exchange rate. In summary, the Wavelet-LSTM model demonstrates strong predictive performance in this scenario, offering accurate forecasts that closely match the actual exchange rate, indicating that it successfully handles both trends and volatility. The graph in Fig. 3 compares the actual and predicted RUB (Russian Ruble) exchange rates using a Wavelet-LSTM model. It can be noted, one key observation is that the predicted values track the overall trend of the actual exchange rate relatively well, especially in the earlier phases (up to around the 40th observation). The model captures the upward trend in the exchange rate accurately, though it tends to smooth out some of the sharper fluctuations. In the later phase of the graph, particularly after the 60th observation, the predicted values start to deviate more from the actual values, missing some of the rapid rises and dips. Overall, while the model is effective at predicting the general trend and long-term movements, it struggles with the more volatile behavior of the Ruble in this case. The predicted line is smoother, which indicates that while the model captures overall direction well, it underestimates the magnitude of short-term fluctuations. The graph in Fig. 4 compares the Actual Brazilian Real Exchange Rate with the Predicted Brazilian Real Exchange Rate using the Wavelet-LSTM method. The horizontal axis represents time, while the vertical axis shows the exchange rate values ranging from 7.6 to 8.8. Throughout the graph, the predicted values closely follow the actual exchange rates, indicating the effectiveness of the Wavelet-LSTM model in forecasting. There are several points where both lines peak and dip simultaneously, suggesting accurate predictions. However, there are also instances where the lines diverge, highlighting areas where the model’s predictions were less accurate. This analysis is crucial for economists and investors who rely on accurate exchange rate forecasts for decision-making. The graph in Fig. 5 , compares the Actual South African Rand Exchange Rate with the Predicted South African Rand Exchange Rate using the Wavelet-LSTM method. The horizontal axis represents time, spanning from 0 to approximately 80 units, while the vertical axis shows the exchange rate values ranging from 25 to 31. Throughout the graph, the predicted values closely follow the actual exchange rates, indicating the effectiveness of the Wavelet-LSTM model in forecasting. The actual exchange rate line has sharper turns and more pronounced peaks, while the predicted rate line appears smoother but follows a similar overall trend. This analysis is crucial for economists and investors who rely on accurate exchange rate forecasts for decision-making. Evaluation Metrics The Table 2 provides evaluation metrics for predicting exchange rates of five BRICS currencies (INR, CNY, RUBLE, BLR, and ZAR) using Wavelet-LSTM model and evaluates the performance on both test and training datasets. The key metrics include Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and R-squared (R²) for both test and train sets, offering insights into the model's accuracy and generalization. For the Indian Rupee (INR), the test MSE is 2009.1 and RMSE is 44.820, which represent the squared and root mean differences between the predicted and actual values. These relatively high error values indicate significant deviations in the model's predictions for the INR. Moreover, the negative R² (-0.5081) on the test set shows that the model performs worse than a simple mean-based prediction, indicating poor fit. However, in the training set, the model performs better with an MSE of 2909.6, an RMSE of 53.940, and a strong R² of 0.9628, suggesting overfitting as the model fits well on the training data but poorly on unseen test data. For the Chinese Yuan (CNY), the model performs well on both test and train sets. The test MSE is 0.0310 and RMSE is 0.1761, indicating very low errors, and the R² of 0.8432 shows that the model explains a large portion of the variance in the data. The performance improves even further on the training set with an MSE of 0.0141, RMSE of 0.1191, and an R² of 0.9771, indicating excellent predictive power with minimal error and high explanatory strength. For the Russian Ruble (RUBLE), the model shows relatively large error values on both the test and train sets due to the high MSE (111,517 on the test set and 203,398 on the train set), resulting in high RMSE values (1056.0 for test and 450.99 for train). Despite the large errors, the R² values of 0.8284 (test) and 0.9708 (train) indicate that the model captures a significant portion of the variance in the data, particularly in the training set, which again suggests possible overfitting. For the Brazilian Real (BLR), the model performs decently, with a test MSE of 0.4518 and RMSE of 0.6722, meaning that the errors are moderate. The R² value of 0.7186 on the test set indicates that the model explains around 72% of the variance, while in the training set, with an MSE of 1.1258 and RMSE of 1.0610, the model performs even better, reflected in a high R² of 0.9814. This shows that the model fits the training data well and generalizes reasonably to the test data. For the South African Rand (ZARSA), the model performs poorly on the test set, with an MSE of 259.73 and RMSE of 16.120, and an R² of -0.0968, indicating that the model is not capturing the relationship between the variables effectively. However, on the training set, the performance is much better, with an MSE of 85.700, RMSE of 9.2570, and an R² of 0.9492, which highlights a strong fit on the training data but a significant drop in accuracy when applied to the test set. In summary, the model tends to perform better on the training data than on the test data across most currencies, suggesting overfitting issues, particularly for INR and ZARSA. The CNY model shows strong predictive performance on both test and training datasets, making it the most reliable among the currencies. Table 2 Evaluation Metrics MSE _Test RMSE _Test R 2_ Test MSE_ Train RMSE_ Train R 2_ Train INR 2009.1 44.823 -0.5080 2909.6 53.941 0.9627 CNY 0.0310 0.1761 0.8432 0.0141 0.1190 0.9771 RBL 111517 1056.0 0.8284 203398 450.99 0.9707 BLR 0.4518 0.6721 0.7186 1.1257 1.0610 0.9813 ZAR 259.73 16.116 -0.0968 85.698 9.2573 0.9492 Source – Author’s Work Conclusion and Implications The analysis of predictive performance for the exchange rates of BRICS currencies (INR, CNY, RUB, BLR, and ZAR) reveals distinct trends in the model's ability to generalize and accurately forecast. The evaluation metrics, including MSE, RMSE, and R², provide valuable insights and highlight key areas for future model improvements and practical applications. The model exhibits overfitting for several currencies, particularly INR and ZAR. While the training set results show strong performance with high R² values, there is a significant drop in test set performance, indicating limited generalization capabilities. This disparity underscores the need for improved regularization and validation techniques to enhance the model’s ability to generalize effectively. In contrast, the Chinese Yuan (CNY) stands out as a benchmark, showing strong performance on both training and test datasets. The model produces low errors and high R² values, suggesting it effectively captures the dynamics of CNY exchange rates and provides a reliable benchmark for robust predictive performance. The model’s predictive accuracy varies considerably across different currencies. For INR and ZAR, poor performance on the test sets suggests that the model struggles to generalize, pointing to potential issues with data structure, feature selection, or model complexity. RUB and BLR show moderate performance, indicating that fine-tuning is required to improve generalization while maintaining strong training set results. The CNY, however, shows reliable predictions, demonstrating that the model is well-suited to certain exchange rate behaviours, likely influenced by smoother patterns or higher-quality data. The findings have several implications for future improvements. First, the presence of overfitting suggests the need for strategies like reducing model complexity, employing regularization techniques, or incorporating cross-validation to improve generalization and prevent over-reliance on training data. Additionally, the poor performance for INR and ZAR may be attributed to noisier or less predictable data, suggesting that enhancing data preprocessing, incorporating additional explanatory variables, or using domain-specific insights could improve predictive accuracy. The varied performance across currencies indicates that a one-size-fits-all approach may not be optimal. Developing currency-specific models tailored to the unique characteristics of each exchange rate could yield better results. In practical terms, stakeholders relying on exchange rate forecasts can have confidence in the model's robustness for CNY, whereas further caution and refinement are necessary for other currencies, particularly INR and ZAR. Future research should explore advanced methods, such as ensemble learning or deep learning approaches, to address overfitting and improve model robustness across all currencies. By addressing the identified limitations and leveraging the insights from CNY’s performance, the model’s applicability can be broadened, ultimately enhancing its utility in forecasting exchange rates in diverse economic contexts. Declarations Author Contributions: Dr. Arushi Mehta conceptualized the study, developed the deep learning framework, conducted the empirical analysis, and wrote the manuscript. All work, including data processing, model development, hyperparameter tuning, and interpretation of results, was performed by the sole author. Funding: This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Conflict of Interest: The author declares that there is no conflict of interest with respect to the publication of this paper. Ethics Approval and Consent to Participate: Not applicable. This study does not involve human participants, animal testing, or the use of personal data. Data Availability Statement: The currency data used in this study were sourced from publicly accessible databases, including central bank and financial data repositories. Further details can be provided upon request. Code Availability: The Python scripts and deep learning model configurations used for forecasting are available from the author upon reasonable request. Declaration of Originality: The author affirms that the work is original, has not been published previously, and is not currently under consideration for publication elsewhere. 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Comput Electron Agric 192:106623 Zeng Y, Chen J, Jin N, Jin X, Du Y (2022) Air quality forecasting with hybrid LSTM and extended stationary wavelet transform. Build Environ 213:108822 Zhang J, Liu H, Bai W, Li X (2024) A hybrid approach of wavelet transform, ARIMA and LSTM model for the share price index futures forecasting. North Am J Econ Finance 69:102022 Additional Declarations The authors declare no competing interests. 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. 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1","display":"","copyAsset":false,"role":"figure","size":96015,"visible":true,"origin":"","legend":"\u003cp\u003eINR Prediction Using Wavelet-LSTM\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-8199826/v1/0d97af17f15ee5baa2f824c2.png"},{"id":96783592,"identity":"cc8e5294-35bd-4ef8-9e53-335874a1ade2","added_by":"auto","created_at":"2025-11-26 05:16:50","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":94100,"visible":true,"origin":"","legend":"\u003cp\u003eCNY Prediction Using Wavelet-LSTM\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-8199826/v1/c037cc856e30184972b40d14.png"},{"id":96915644,"identity":"a6a593b0-a287-4bbf-8afb-4c2a69d260f2","added_by":"auto","created_at":"2025-11-27 14:07:27","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":98827,"visible":true,"origin":"","legend":"\u003cp\u003eRUBLE Prediction Using Wavelet-LSTM\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-8199826/v1/35daf4031a0d55faaaa8b06c.png"},{"id":96783599,"identity":"1e9cc22a-1206-477a-9ad3-79f7169ebb33","added_by":"auto","created_at":"2025-11-26 05:16:50","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":135333,"visible":true,"origin":"","legend":"\u003cp\u003eBLR Prediction Using Wavelet-LSTM\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-8199826/v1/11c227e9a55adda2eeafdcbf.png"},{"id":96783600,"identity":"303d616f-98e8-402e-8ca4-c96a18e9d147","added_by":"auto","created_at":"2025-11-26 05:16:50","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":133759,"visible":true,"origin":"","legend":"\u003cp\u003eSouth African Prediction Using Wavelet-LSTM\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-8199826/v1/e15457b70e1a5f348070086f.png"},{"id":97135438,"identity":"d617c740-fc97-4c37-a178-033a73b742ad","added_by":"auto","created_at":"2025-12-01 09:46:03","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":951135,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8199826/v1/6758f6a6-acea-4e4d-823d-c6a0fdc65481.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eWavelet-Driven LSTM Modelling for Exchange Rate Forecasting in BRICS Economies\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe prediction of exchange rates in BRICS countries (Brazil, Russia, India, China, and South Africa) holds significant importance in the current global geopolitical environment, given their critical roles in global trade, investment flows, and economic alliances. The geopolitical risk is key determinant of variations in financial markets and investment related decisions (Pastor and Veronesi, 2013). BRICS countries are recipient of global investment from the major countries like Japan, USA, and Germany (Sui and Sun, \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), are affected by the investment flows from abroad, and exchange rate regime followed. Exchange rate fluctuations directly impact trade balances, affecting export competitiveness and import costs. In a world where BRICS countries are deepening their trade ties and economic cooperation, predicting exchange rates allows businesses to manage risks and optimize profits. BRICS group consists 42 percent of world population, 23 per cent of GDP, 30 per cent of territory, and 18 per cent of trade (Salisu et al., 2022\u003csup\u003ea\u003c/sup\u003e). Additionally, the geopolitical tensions, such as Russia\u0026rsquo;s involvement in the Ukraine war and rising U.S.-China rivalries, have added uncertainty to exchange rate movements. Accurate predictions help governments and businesses mitigate these risks, maintaining stability in trade and pricing.\u003c/p\u003e\u003cp\u003eAmid the ongoing internationalisation of BRICS currencies, de-dollarization and discussions around a potential common BRICS currency, accurate forecasting can strengthen the feasibility of its introduction (Coquid\u0026eacute; et al. \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Kondratov, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Das and Roy, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Ahmed et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Atif et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Ahmed, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2025\u003c/span\u003ec). Moreover, exchange rates influence inflation by affecting the costs of imported goods, which is particularly sensitive for BRICS nations like Brazil and South Africa. Predicting exchange rate trends enables central banks to craft monetary policies that control inflation and stabilize economies. BRICS members are also exploring currency cooperation, including discussions on a common currency, making exchange rate forecasts vital for assessing the feasibility and impact of such initiatives. Investors rely on these predictions to assess the risks and returns of foreign direct investment (FDI) and portfolio investments. Currency volatility can deter investment or cause capital flight, making stable forecasts essential for attracting and retaining capital inflows. For resource-dependent BRICS countries, such as Russia, Brazil, and South Africa, exchange rate forecasts are also critical for predicting commodity prices and revenues, especially in response to global demand shifts. Governments and central banks rely heavily on exchange rate predictions for policy formulation and economic planning, influencing interest rates, trade tariffs, and fiscal strategies. As BRICS nations seek to position themselves in a more multipolar world, the ability to accurately predict exchange rates has become both an economic and geopolitical necessity (Salisu et al., 2021\u003csup\u003eb\u003c/sup\u003e).\u003c/p\u003e\u003cp\u003eTraditional econometric methods, such as ARIMA, VAR, and GARCH, have been widely used to forecast exchange rates. However, these methods face several challenges such as linear assumption, as the movement of forex rates is complex, and nonlinear due to factors such as interest rates, inflation, geopolitical events, and market sentiment. The traditional model flexibility with big data is limited, and often fail to account for external shocks (Ramos-P\u0026eacute;rez et al. \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Liu, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Pradeepkumar and Ravi, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). The assumption of stationarity, that statistical properties are constant over the time, is also limitation of traditional models, along with the model specification such as lag length, autocorrelation etc.\u003c/p\u003e\u003cp\u003eIn recent, the literature around time series forecasting using Artificial Intelligence (AI) has grown significantly. Machine learning ML, and DL models, such as ANNs, random forests, and SVMs, offer several advantages over traditional econometric methods in predicting exchange rates. The ML models excel at capturing complex and nonlinear linkages and can detect hidden patterns in data (Srivastava et al. \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Rubio et al \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Kamalov et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Further, the machine learning models can process the large datasets, incorporating multiple factors. The ML and DL based models can also adapt to non-stationary data. The RNNs or LSTM technique are efficient in handling the time series with changing patterns. The AI based models can be trained on high-frequency data, enhancing the ability to handle the external shocks. Further, the Automatic feature selection, robustness and flexibility, and overall improved forecast accuracy. Due to this, the ML techniques are increasingly becoming a preferred approach for exchange rate forecasting in the evolving global financial environment (Zhang et al. \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eA promising approach to address this complexity is the utilization of Wavelet-LSTM networks. This hybrid model integrates the advantages of wavelet analysis, which facilitates the decomposition of time series data into distinct frequency components, with the robust sequential learning capabilities of LSTM neural networks (Tamilselvi et al. \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Chen et al. \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). By employing this methodology, researchers can effectively capture both long-term trends and short-term fluctuations in BRICS forex rates, potentially enhancing forecast accuracy. The wavelet decomposition process contributes to the management of non-stationary data and the reduction of noise, while the LSTM network demonstrates proficiency in learning intricate temporal dependencies. This approach may prove particularly valuable for policymakers, investors, and financial institutions operating within BRICS countries, as it has the potential to yield more reliable predictions of forex rate movements in these volatile markets. Forecasting foreign exchange (forex) rates in BRICS economies presents a significant challenge due to the dynamic nature of these emerging markets. The complexity of these economies, characterized by rapid growth, evolving financial systems, and susceptibility to global economic shifts, necessitates sophisticated forecasting techniques. A promising approach to address this complexity is the utilization of Wavelet LSTM networks. This hybrid model integrates the advantages of wavelet analysis, which facilitates the decomposition of time series data into distinct frequency components, with the robust sequential learning capabilities of LSTM neural networks.\u003c/p\u003e\u003cp\u003eThis methodology captures both long-term trends and short-term fluctuations in BRICS forex rates can be captured, potentially enhancing forecast accuracy. The wavelet decomposition process contributes to the management of non-stationary data and the reduction of noise, which are common challenges in forex rate analysis. This step allows for a more nuanced examination of the underlying patterns in the time series data, separating high-frequency fluctuations from low-frequency trends. Such decomposition can reveal hidden structures within the data that might be obscured in traditional time series analysis methods. The LSTM network, a specialized form of recurrent neural network, demonstrates proficiency in learning intricate temporal dependencies. This capability is particularly valuable in forex rate prediction, where complex interactions between various economic factors, geopolitical events, and market sentiments influence exchange rates over different time horizons. LSTM networks can effectively capture and remember relevant information over extended periods, making them well-suited for identifying long-term dependencies in forex rate movements. The combination of wavelet analysis and LSTM networks in this hybrid approach offers several advantages. Firstly, it allows for the simultaneous consideration of multiple time scales, from short-term fluctuations to long-term trends, providing a more comprehensive view of forex rate dynamics. Secondly, the noise reduction achieved through wavelet decomposition can lead to more stable and reliable input features for the LSTM network, potentially improving the overall predictive performance.\u003c/p\u003e\u003cp\u003eThis approach is valuable particularly, for policymakers, investors, and financial institutions operating within BRICS countries, as it has the potential to yield more reliable predictions of forex rate movements in these volatile markets. Policymakers can utilize these forecasts to inform monetary policy decisions and manage currency stability. Investors and traders can leverage the predictions to optimize their portfolio strategies and manage risk exposure in BRICS currencies. Financial institutions can enhance their risk management practices and improve their foreign exchange operations based on more accurate forecasts. Moreover, the application of Wavelet LSTM networks to BRICS forex rate forecasting opens up avenues for further research and development in the field of financial time series analysis. Researchers can explore variations of this hybrid model, such as incorporating additional economic indicators or experimenting with different wavelet transformation techniques to further refine the forecasting accuracy. The success of this approach in BRICS economies could also pave the way for its application in other emerging markets or even developed economies, contributing to the broader field of economic forecasting and financial modelling.\u003c/p\u003e"},{"header":"Literature Review","content":"\u003cp\u003eThe use of machine learning and deep learning has grown significantly in the prediction of the time series variables(Ahmed, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2025\u003c/span\u003ea, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2025\u003c/span\u003eb, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2025\u003c/span\u003ed, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2025\u003c/span\u003ee). The use of ML and DL has advantages of accuracy and capturing the non-linearity and complexity of the time series variables, irrespective of the stationarity and normality, the necessary assumptions of the many traditional methods of forecasting. The review study by, Junior et al. (2023) provides, comprehensive background of the previous research in the forex market forecasting, whereas the Liu and Wang (\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), reviewed ML and DL models used in the time series prediction.\u003c/p\u003e\u003cp\u003eThe selection of model and evaluation is crucial in accurate prediction. To probe this question, Junior et al. (2023) reviewed the literature of forex forecasting methodologies. In reviewing of 60 studies from 2010 to 2021, authors found use of LSTM and ANN models to be most commonly used algorithm of machine learning. Further, authors found that MSE, RMSE, MAE, and MAPE were the most commonly used evaluation metrics. Authors concluded that there is significant scope of research in the exchange rate prediction. As per Fletcher (\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2012\u003c/span\u003e), the SVM, Relevance Vector Machine (RVM) and Neural Network shows improved results when exogenous variables, affecting the basket of forex returns are included. Panda et al. (\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) reviewed the advance exchange rate prediction of studies from 2000 to 2019. The author found the use of different models such as ANN, FLANN, HMM, SVM, and AR models.\u003c/p\u003e\u003cp\u003eIslam et al. (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) examined the studies which have studied the advancements in forex prediction. Based on the analysis of 39 studies from select publishers, author found the use of neural networks, GRU and LSTM to be most prevalent in the forecasting of exchange rates. In their review, Sezer et al. (\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) indicated increased use of DL methods in time series forecasting. Berradi et al. (2020) favoured the deep learning techniques over the traditional ones in the forecasting of time series. The study further found that RNNs are mostly used model in the predictions. Ryll and Siedens (2019) evaluated the machine learning models from 150 research papers, and found them to be outperforming the traditional models. Further, among the findings, the RNN models perform better than the feed forward neural network as well as SVM. The findings hinted at the temporal effect in prediction across the assets and location, and can be utilised in forecasting of time series. Henriques et al. (2019) recognised the difficulty in forecasting the financial time series due to chaotic, non-linear and dynamic nature of them. Further in the findings of bibliometric analysis, SVM and neural networks are the dominantly used ML models, and data is mostly used from north American markets. Authors suggested the relevancy of the research field, and required focus on the data of emerging markets.\u003c/p\u003e\u003cp\u003eAbedin et al. (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) proposed a model by combining the bagging ridge regression and Bi-LSTM model to predict the forex rate of 21 currencies before the Covid and after the Covid. Further, the authors compared the models with the traditional models such as SVM, Decision Tree, random forest as well as DL methods of LSTM and Bi-LSTM. The proposed model was found to be more accurate, however, the accuracy varied before and during the pandemic. Dautel et al. (\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) compared the LSTM and GRU with the traditional recurrent network architecture and feedforward network in directional forecasting. The authors found the DL methods to be suitable in prediction, but also pointed out the difficulty in tuning and implementing the architectures. Rabbi et al. (\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) forecasted the currencies of 22 countries by using the various ML and DL techniques. Out of the SVR, and RVR, and LSTM. The LSTM is found to be the more accurate as compared to the others. Datta et al. (\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) proposed different ML and DL models in prediction of 22 currencies. The study employed the lasso regression, decision tree, ridge regression, and the Bi-LSTM in prediction, and found the Bi-LSTM to be better performing as compared to the other models. The MAE, MSE, RMSE, and MAPE were used to evaluate the model accuracy.\u003c/p\u003e\u003cp\u003eInce and Trafalis (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) proposed forecasting model combining the parametric and non-parametric test such as ARIMA and VAR, with the SVR and ANN. The study found the SVR technique to be accurate in performance. Wang et al. (\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) proposed the CNN-TLSTM model in prediction of Canadian dollar. The CNN model selects the features whereas the TLSTM does the prediction of time series. In comparison of MLP, CNN, RNN, LSTM and CNN-LSTM, the CNN-LSTM model is found to be better predictor of the Chinese Yuan forex rate. Wang and Chen (\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) combine the two-stage feature extraction model and Adaboost based reinforcement ensemble learning framework. The resultant deep RNN, is found to be a better in accuracy. Islam and Hossain (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) combined the LSTM and GRU to predict the four commonly used currencies, EUR, GBP, CAD, and CHF. The author also compared the model with the standalone LSTM and GRU. on the basis of MSE, RMSE, MAE, and R-Squared, the study found the combined LSTM-GRU model to be best performing.\u003c/p\u003e\u003cp\u003eOn the basis of the analysis of above, it can be noticed that literature has been in the favour of deep learning in forecasting of the time series data. Further, it can be observed that, the use of combination of traditional and deep learning models is lacking in time series forecasting. The wavelet LSTM model is widely used in forecasting of various type of variables, such as wind power, fault in power grids, solar irradiance, electricity price prediction, stock market prediction, fault detection in rotating machinery, air quality, electricity consumption (Liu et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Branco et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Chang et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Jalayer et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Zeng et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Chi, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). However, the use wavelet LSTM in forex rate forecasting has not been observed in the literature. To the best of authors knowledge, no study has applied the combined approach of Wavelet-LSTM in forex rate prediction. This study probes the predictive accuracy of this ensemble model this paper. This study aims to investigate the predictive accuracy of a Wavelet Transformed LSTM model in forecasting forex rates for the BRICS countries. By combining the signal processing capabilities of wavelets with the powerful temporal learning abilities of LSTM, this novel approach may provide valuable insights and improved forecasting performance compared to existing methods.\u003c/p\u003e"},{"header":"Methods and Materials","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003cdiv id=\"Sec4\" class=\"Section3\"\u003e\u003ch2\u003eData\u003c/h2\u003e\u003cp\u003eThe data consists the crude oil prices and forex rate of five BRICS countries. The variables are OIL \u0026ndash; Brent crude oil prices, INR-Indian Rupee, CNY- Chinese Yuan, RUBLE- Russian Ruble, and ZARSA denotes South African Rand.\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\u003e\u0026ndash; Descriptive Statistics\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\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eOIL\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eINR\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eCNY\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eRUBLE\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eBLR\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eZARSA\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMean\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e72.075\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e69.629\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e6.6150\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e62.636\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e3.9085\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e14.152\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eStd. Error\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.4392\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.1372\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.0064\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.2997\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.0207\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.0480\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMedian\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e68.695\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e68.660\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e6.6061\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e64.092\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e3.8211\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e14.261\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMode\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e70.710\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e64.860\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e7.1942\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e32.985\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e5.1706\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e14.485\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eStd. Dev\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e23.688\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e7.3999\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.3452\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e16.164\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1.1214\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e2.5887\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSam. Var\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e561.14\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e54.758\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.1192\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e261.28\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1.2575\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e6.7015\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eKurtosis\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e-0.7537\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-0.6437\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-1.1339\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.4219\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e-1.2346\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e-0.5920\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSkewness\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.2884\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.1669\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.1397\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-0.2314\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e-0.0354\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.0014\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRange\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e124.06\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e30.391\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.3063\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e113.13\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e3.9445\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e11.347\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMinimum\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e9.1200\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e53.035\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e6.0412\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e29.863\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1.9447\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e8.4580\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMaximum\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e133.18\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e83.426\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e7.3475\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e143.00\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e5.8892\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e19.805\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\n\u003ch3\u003eSource – Author’s Work\u003c/h3\u003e\n\u003cp\u003eThe descriptive statistics for the five BRICS currencies (INR, CNY, RUBLE, BLR, and ZARSA) and oil prices reveal important insights into their central tendencies, dispersion, and distribution shapes. The mean values show that oil prices averaged \u003cspan\u003e$\u003c/span\u003e72.08, while the Indian Rupee (INR) averaged 69.63, the Chinese Yuan (CNY) 6.62, the Russian Ruble (RUBLE) 62.64, the Brazilian Real (BLR) 3.91, and the South African Rand (ZARSA) 14.15 per US Dollar. Among these currencies, the CNY exhibited the least fluctuation around its mean with a small standard error of 0.0064, indicating its relative stability, while the RUBLE had the largest standard error of 0.2998, signifying greater variability in its average exchange rate.\u003c/p\u003e\u003cp\u003eStandard deviation (a measure of dispersion) and variance (the square of standard deviation) further highlight the variability of these currencies. The RUBLE shows the highest standard deviation (16.16) and variance (261.29), confirming its status as the most volatile currency in the group. In contrast, the CNY has the smallest standard deviation (0.345) and variance (0.119), underscoring its stability. The INR and ZARSA show moderate variability, with standard deviations of 7.40 and 2.59, respectively. When examining kurtosis, the most currencies, including the INR, CNY, BLR, and ZARSA, have negative kurtosis values, indicating flatter distributions with fewer extreme values. The RUBLE, with a slightly positive kurtosis (0.42), indicates a higher likelihood of extreme values or outliers in its data. Skewness, which measures asymmetry in the data, is generally close to zero for most currencies, with the INR, CNY, and ZARSA showing slightly positive skewness, suggesting a nearly symmetric distribution but with a slight tilt towards higher values. On the other hand, the RUBLE and BLR exhibit slight negative skewness, meaning their distributions have more frequent lower values.\u003c/p\u003e\n\u003ch3\u003eWavelet – LSTM\u003c/h3\u003e\n\u003cp\u003eWavelet Long Short-Term Memory (Wavelet LSTM) is a hybrid model that combines wavelet transform techniques with Long Short-Term Memory (LSTM) neural networks to enhance time-series forecasting. The wavelet transform decomposes the original time-series data into different frequency components, allowing the model to focus on both short-term fluctuations and long-term trends separately. By capturing both high and low-frequency information, Wavelet LSTM improves the model's ability to predict complex time-series patterns more effectively than traditional LSTM models, which may struggle with multi-scale data.\u003c/p\u003e\u003cp\u003eThe process typically involves applying the discrete wavelet transform (DWT) to decompose the input time-series \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:x\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e into approximation (A) and detail (D) coefficients at different levels of decomposition. These components are then fed into separate LSTM models, which are specialized in learning temporal dependencies from each frequency band. The outputs of the LSTM models are then aggregated, often by reconstructing the signal through an inverse wavelet transform (IWT), to provide the final forecast.\u003c/p\u003e\u003cp\u003eMathematically, the wavelet decomposition of the time-series \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:x\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e can be expressed as:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:x\\left(t\\right)=A\\left(t\\right)+D\\left(t\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:A\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e represents the low-frequency components (approximation), and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:D\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e represents the high-frequency components (details). These components are then processed individually through LSTM layers to predict future values:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:\\widehat{y}\\left(t\\right)={LSTM}_{A}\\left(A\\left(t\\right)\\right)+{LSTM}_{D}\\left(D\\left(t\\right)\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eFinally, the predicted components are combined to form the overall forecast. The Wavelet LSTM approach is particularly useful in scenarios with complex, noisy, or multi-scale data, such as financial markets, where different time frames may show distinct patterns.\u003c/p\u003e\u003cp\u003eEvaluating models goes beyond simply checking their accuracy; it's about assessing their reliability in making predictions. The accuracy and reliability are crucial in making forecast. There are various metrics which evaluate the models, including MSE, RMSE, and R-squared. Various studies have used the MSE, RMSE, and R-Square for the evaluation of forecasting accuracy of the machine learning models (Alqahtani \u0026amp; Abdelhafez, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Aziz et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Chen, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Kandil et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Muganda \u0026amp; Kasamani, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Nanthiya et al., \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Prakash \u0026amp; Singh, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Ahmed and Kaur, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2025\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eIn machine learning, MSE and RMSE gauge how accurate a model's predictions are by capturing the average difference among forecasted and observed values. MSE acts like a trainer during the learning process, guiding the model to minimize this error. It excels at penalizing the large mistakes because it penalizes huge differences more heavily. However, MSE is measured in squared units, different from the target variable's unit, making interpretation a bit complex. To address this, RMSE simply takes the root square of MSE, presenting the error in the same units as the target variable for easier understanding. Both metrics are popular for their focus on large errors but are also sensitive to outliers, so keep the target variable's unit in mind when evaluating the error values. The R squared focuses on the part of variance explained in the dependent variable by the model. It essentially quantifies how well the model fits the data, indicating the degree to which it can explain the target variable's variance. R-squared is an easy-to-understand measure of model fit, and varies from zero to one, where one signifies a perfect fit. While it's scale-independent, adding more predictors can artificially inflate R-squared. Importantly, R-squared about the model's predictive power; it simply helps us understand the proportion of variance explained by the factors considered in the model.\u003c/p\u003e"},{"header":"Results and Findings","content":"\u003cp\u003eThe graph in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e illustrates a comparison between the actual and predicted INR exchange rates of test data using a Wavelet-LSTM model. The data was split in ratio of 80:20. The test data predictions are based on the trained data by the used algorithm. The blue line represents the actual exchange rate, showing real-world fluctuations over time, marked by periods of sharp increases and decreases. In contrast, the orange line represents the model's predictions, which, while capturing the general trend, appear much smoother and show fewer sharp fluctuations than the actual data. From graph, it can be observed that is the underestimation of volatility by the Wavelet-LSTM model. Although the model successfully tracks the overall trend, it struggles to predict the more rapid and extreme changes in the exchange rate. The predicted line, while aligned with the overall direction of movement, fails to capture the sharp spikes or dips that are evident in the actual data. This suggests that the model captures long-term trends effectively but may need further refinement to accurately model short-term volatility. Overall, the Wavelet-LSTM model performs well in forecasting general trends but leaves room for improvement in handling rapid and complex fluctuations in exchange rates.\u003c/p\u003e\u003cp\u003eThe graph in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e indicate the predicted and actual values of Chinese Yuan. The blue line represents the actual CNY exchange rate, showing its real fluctuations over time. In this case, the model appears to perform well, closely following the actual exchange rate movements with a good degree of accuracy. The model tracks trends and volatility, with the predicted line closely mirroring the peaks, troughs, and general direction of the actual data. While there are some minor discrepancies, particularly around the sharper changes in the exchange rate, the predicted values align well with the overall pattern of the actual exchange rate. This suggests that the Wavelet-LSTM model is effectively capturing both short-term fluctuations and long-term trends in the CNY exchange rate. In summary, the Wavelet-LSTM model demonstrates strong predictive performance in this scenario, offering accurate forecasts that closely match the actual exchange rate, indicating that it successfully handles both trends and volatility.\u003c/p\u003e\u003cp\u003eThe graph in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e compares the actual and predicted RUB (Russian Ruble) exchange rates using a Wavelet-LSTM model. It can be noted, one key observation is that the predicted values track the overall trend of the actual exchange rate relatively well, especially in the earlier phases (up to around the 40th observation). The model captures the upward trend in the exchange rate accurately, though it tends to smooth out some of the sharper fluctuations. In the later phase of the graph, particularly after the 60th observation, the predicted values start to deviate more from the actual values, missing some of the rapid rises and dips. Overall, while the model is effective at predicting the general trend and long-term movements, it struggles with the more volatile behavior of the Ruble in this case. The predicted line is smoother, which indicates that while the model captures overall direction well, it underestimates the magnitude of short-term fluctuations.\u003c/p\u003e\u003cp\u003eThe graph in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e compares the Actual Brazilian Real Exchange Rate with the Predicted Brazilian Real Exchange Rate using the Wavelet-LSTM method. The horizontal axis represents time, while the vertical axis shows the exchange rate values ranging from 7.6 to 8.8. Throughout the graph, the predicted values closely follow the actual exchange rates, indicating the effectiveness of the Wavelet-LSTM model in forecasting. There are several points where both lines peak and dip simultaneously, suggesting accurate predictions. However, there are also instances where the lines diverge, highlighting areas where the model\u0026rsquo;s predictions were less accurate. This analysis is crucial for economists and investors who rely on accurate exchange rate forecasts for decision-making.\u003c/p\u003e\u003cp\u003eThe graph in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, compares the Actual South African Rand Exchange Rate with the Predicted South African Rand Exchange Rate using the Wavelet-LSTM method. The horizontal axis represents time, spanning from 0 to approximately 80 units, while the vertical axis shows the exchange rate values ranging from 25 to 31. Throughout the graph, the predicted values closely follow the actual exchange rates, indicating the effectiveness of the Wavelet-LSTM model in forecasting. The actual exchange rate line has sharper turns and more pronounced peaks, while the predicted rate line appears smoother but follows a similar overall trend. This analysis is crucial for economists and investors who rely on accurate exchange rate forecasts for decision-making.\u003c/p\u003e\u003cdiv id=\"Sec13\" class=\"Section3\"\u003e\u003ch2\u003eEvaluation Metrics\u003c/h2\u003e\u003cp\u003eThe Table \u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e provides evaluation metrics for predicting exchange rates of five BRICS currencies (INR, CNY, RUBLE, BLR, and ZAR) using Wavelet-LSTM model and evaluates the performance on both test and training datasets. The key metrics include Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and R-squared (R\u0026sup2;) for both test and train sets, offering insights into the model's accuracy and generalization.\u003c/p\u003e\u003cp\u003eFor the Indian Rupee (INR), the test MSE is 2009.1 and RMSE is 44.820, which represent the squared and root mean differences between the predicted and actual values. These relatively high error values indicate significant deviations in the model's predictions for the INR. Moreover, the negative R\u0026sup2; (-0.5081) on the test set shows that the model performs worse than a simple mean-based prediction, indicating poor fit. However, in the training set, the model performs better with an MSE of 2909.6, an RMSE of 53.940, and a strong R\u0026sup2; of 0.9628, suggesting overfitting as the model fits well on the training data but poorly on unseen test data. For the Chinese Yuan (CNY), the model performs well on both test and train sets. The test MSE is 0.0310 and RMSE is 0.1761, indicating very low errors, and the R\u0026sup2; of 0.8432 shows that the model explains a large portion of the variance in the data. The performance improves even further on the training set with an MSE of 0.0141, RMSE of 0.1191, and an R\u0026sup2; of 0.9771, indicating excellent predictive power with minimal error and high explanatory strength.\u003c/p\u003e\u003cp\u003eFor the Russian Ruble (RUBLE), the model shows relatively large error values on both the test and train sets due to the high MSE (111,517 on the test set and 203,398 on the train set), resulting in high RMSE values (1056.0 for test and 450.99 for train). Despite the large errors, the R\u0026sup2; values of 0.8284 (test) and 0.9708 (train) indicate that the model captures a significant portion of the variance in the data, particularly in the training set, which again suggests possible overfitting. For the Brazilian Real (BLR), the model performs decently, with a test MSE of 0.4518 and RMSE of 0.6722, meaning that the errors are moderate. The R\u0026sup2; value of 0.7186 on the test set indicates that the model explains around 72% of the variance, while in the training set, with an MSE of 1.1258 and RMSE of 1.0610, the model performs even better, reflected in a high R\u0026sup2; of 0.9814. This shows that the model fits the training data well and generalizes reasonably to the test data. For the South African Rand (ZARSA), the model performs poorly on the test set, with an MSE of 259.73 and RMSE of 16.120, and an R\u0026sup2; of -0.0968, indicating that the model is not capturing the relationship between the variables effectively. However, on the training set, the performance is much better, with an MSE of 85.700, RMSE of 9.2570, and an R\u0026sup2; of 0.9492, which highlights a strong fit on the training data but a significant drop in accuracy when applied to the test set.\u003c/p\u003e\u003cp\u003eIn summary, the model tends to perform better on the training data than on the test data across most currencies, suggesting overfitting issues, particularly for INR and ZARSA. The CNY model shows strong predictive performance on both test and training datasets, making it the most reliable among the currencies.\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\u003eEvaluation Metrics\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=\"left\" 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=\"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=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\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\u003eMSE _Test\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eRMSE _Test\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eR\u003csup\u003e2_\u003c/sup\u003eTest\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eMSE_ Train\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eRMSE_ Train\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eR\u003csup\u003e2_\u003c/sup\u003eTrain\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eINR\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e2009.1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e44.823\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-0.5080\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e2909.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e53.941\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.9627\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCNY\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.0310\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.1761\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.8432\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.0141\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.1190\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.9771\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRBL\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e111517\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1056.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.8284\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e203398\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e450.99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.9707\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eBLR\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.4518\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.6721\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.7186\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.1257\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1.0610\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.9813\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eZAR\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e259.73\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e16.116\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-0.0968\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e85.698\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e9.2573\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.9492\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\u003cp\u003eSource \u0026ndash; Author\u0026rsquo;s Work\u003c/p\u003e\u003c/div\u003e"},{"header":"Conclusion and Implications","content":"\u003cdiv id=\"Sec15\" class=\"Section3\"\u003e\u003cp\u003eThe analysis of predictive performance for the exchange rates of BRICS currencies (INR, CNY, RUB, BLR, and ZAR) reveals distinct trends in the model's ability to generalize and accurately forecast. The evaluation metrics, including MSE, RMSE, and R\u0026sup2;, provide valuable insights and highlight key areas for future model improvements and practical applications.\u003c/p\u003e\u003cp\u003eThe model exhibits overfitting for several currencies, particularly INR and ZAR. While the training set results show strong performance with high R\u0026sup2; values, there is a significant drop in test set performance, indicating limited generalization capabilities. This disparity underscores the need for improved regularization and validation techniques to enhance the model\u0026rsquo;s ability to generalize effectively. In contrast, the Chinese Yuan (CNY) stands out as a benchmark, showing strong performance on both training and test datasets. The model produces low errors and high R\u0026sup2; values, suggesting it effectively captures the dynamics of CNY exchange rates and provides a reliable benchmark for robust predictive performance. The model\u0026rsquo;s predictive accuracy varies considerably across different currencies. For INR and ZAR, poor performance on the test sets suggests that the model struggles to generalize, pointing to potential issues with data structure, feature selection, or model complexity. RUB and BLR show moderate performance, indicating that fine-tuning is required to improve generalization while maintaining strong training set results. The CNY, however, shows reliable predictions, demonstrating that the model is well-suited to certain exchange rate behaviours, likely influenced by smoother patterns or higher-quality data.\u003c/p\u003e\u003cp\u003eThe findings have several implications for future improvements. First, the presence of overfitting suggests the need for strategies like reducing model complexity, employing regularization techniques, or incorporating cross-validation to improve generalization and prevent over-reliance on training data. Additionally, the poor performance for INR and ZAR may be attributed to noisier or less predictable data, suggesting that enhancing data preprocessing, incorporating additional explanatory variables, or using domain-specific insights could improve predictive accuracy. The varied performance across currencies indicates that a one-size-fits-all approach may not be optimal. Developing currency-specific models tailored to the unique characteristics of each exchange rate could yield better results. In practical terms, stakeholders relying on exchange rate forecasts can have confidence in the model's robustness for CNY, whereas further caution and refinement are necessary for other currencies, particularly INR and ZAR. Future research should explore advanced methods, such as ensemble learning or deep learning approaches, to address overfitting and improve model robustness across all currencies. By addressing the identified limitations and leveraging the insights from CNY\u0026rsquo;s performance, the model\u0026rsquo;s applicability can be broadened, ultimately enhancing its utility in forecasting exchange rates in diverse economic contexts.\u003c/p\u003e\u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003eAuthor Contributions:\u003c/p\u003e\n\u003cp\u003eDr. Arushi Mehta conceptualized the study, developed the deep learning framework, conducted the empirical analysis, and wrote the manuscript. All work, including data processing, model development, hyperparameter tuning, and interpretation of results, was performed by the sole author.\u003c/p\u003e\n\u003cp\u003eFunding:\u003c/p\u003e\n\u003cp\u003eThis research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.\u003c/p\u003e\n\u003cp\u003eConflict of Interest:\u003c/p\u003e\n\u003cp\u003eThe author declares that there is no conflict of interest with respect to the publication of this paper.\u003c/p\u003e\n\u003cp\u003eEthics Approval and Consent to Participate:\u003c/p\u003e\n\u003cp\u003eNot applicable. This study does not involve human participants, animal testing, or the use of personal data.\u003c/p\u003e\n\u003cp\u003eData Availability Statement:\u003c/p\u003e\n\u003cp\u003eThe currency data used in this study were sourced from publicly accessible databases, including central bank and financial data repositories. Further details can be provided upon request.\u003c/p\u003e\n\u003cp\u003eCode Availability:\u003c/p\u003e\n\u003cp\u003eThe Python scripts and deep learning model configurations used for forecasting are available from the author upon reasonable request.\u003c/p\u003e\n\u003cp\u003eDeclaration of Originality:\u003c/p\u003e\n\u003cp\u003eThe author affirms that the work is original, has not been published previously, and is not currently under consideration for publication elsewhere. All sources used have been appropriately acknowledged.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAbedin MZ, Moon MH, Hassan MK, Hajek P (2021) Deep learning-based exchange rate prediction during the COVID-19 pandemic. Ann Oper Res, 1\u0026ndash;52\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eAhmed H (2025) Is It Getting Green? Insights into Green Bond Influence on Stock Markets of Major Oil-Exporting Countries (September 01, 2025). 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North Am J Econ Finance 69:102022\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"New Delhi Institute of Management","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":"Neural Networks, Forex, Forecasting, BRICS, Wavelet","lastPublishedDoi":"10.21203/rs.3.rs-8199826/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8199826/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cem\u003eThis study evaluates the predictive performance of Wavelet-LSTM models in forecasting exchange rates for BRICS currencies (INR, CNY, RUB, BLR, and ZAR). The data period studied is from March 2013 to February 2024. The analysis reveals significant variability in model performance, with the Chinese Yuan (CNY) exhibiting robust predictive accuracy, as indicated by low errors and high R² values on both training and test datasets. Conversely, the Indian Rupee (INR) and South African Rand (ZAR) show poor test set performance, highlighting overfitting and limited generalization capabilities. Moderate performance for the Russian Ruble (RUB) and Brazilian Real (BLR) suggests potential for improvement through fine-tuning. These findings underscore the need for strategies such as regularization, cross-validation, and enhanced data preprocessing to address overfitting and improve generalization. A tailored, currency-specific modelling approach is recommended to account for diverse exchange rate dynamics. Future research should explore advanced techniques, including ensemble learning, to enhance model robustness and applicability across varying economic contexts.\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eJEL Classification - C45, F31, C53, O57\u003c/em\u003e\u003c/p\u003e","manuscriptTitle":"Wavelet-Driven LSTM Modelling for Exchange Rate Forecasting in BRICS Economies","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-26 05:16:45","doi":"10.21203/rs.3.rs-8199826/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":"7eb6b22f-9ad5-4e41-8471-8d5ea800b395","owner":[],"postedDate":"November 26th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":58558896,"name":"Macroeconomics"}],"tags":[],"updatedAt":"2025-11-26T05:16:46+00:00","versionOfRecord":[],"versionCreatedAt":"2025-11-26 05:16:45","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8199826","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8199826","identity":"rs-8199826","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}