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, 2025c). 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.

The use of machine learning and deep learning has grown significantly in the prediction of the time series variables(Ahmed, 2025a, 2025b, 2025d, 2025e). 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.

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 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 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 can be expressed as:

Where represents the low-frequency components (approximation), and represents the high-frequency components (details). These components are then processed individually through LSTM layers to predict future values:

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.

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.