The challenge the researchers set out to address is structural. Exchange-rate returns may exhibit linear dependence, nonlinear relationships, regime-switching behavior, and volatility clustering, often simultaneously. Classical linear models such as ARIMA capture short-term linear dynamics but collapse when data turn complex. Nonlinear and machine learning methods handle intricate patterns but their superiority is not universal, and gains often prove sample-specific. The authors therefore built an Adaptive Time-Varying Weighted Hybrid Forecasting framework, abbreviated ATW-HyF, that combines three complementary paradigms: ARIMA for linear temporal dependence, a two-regime SETAR model for threshold-driven regime switching, and a feedforward artificial neural network for nonlinear approximation.

The genuinely novel element lies in how the framework weights its components. Conventional hybrid models rely on fixed or equal weights, implicitly assuming that model performance remains stable over time, an assumption rarely satisfied in foreign exchange markets. ATW-HyF instead updates inverse-RMSE weights recursively over a rolling window of twenty forecast errors. Models that recently produced lower errors receive larger performance scores and greater influence in the convex combination, while unreliable components are demoted automatically. The mechanism is grounded in the classical theory of optimal forecast combination, which holds that combining multiple forecasts under the minimum-variance principle reduces forecast uncertainty relative to any individual model.

The framework comes in two versions. ATW-HyF A produces adaptive point forecasts by dynamically combining the one-step-ahead predictions of ARIMA, SETAR, and ANN. ATW-HyF B extends this architecture with a GARCH(1,1) volatility layer that models the conditional variance of the hybrid forecast residuals, capturing volatility clustering and time-varying forecast uncertainty. The result is a unified mean-variance forecasting system that jointly predicts both the direction of exchange-rate returns and the evolving uncertainty surrounding them, information that matters for risk management applications such as Value-at-Risk and Expected Shortfall.

Evaluation was rigorous. The researchers employed an expanding rolling-origin, or walk-forward, procedure in which models are re-estimated at every forecast origin using only past observations, eliminating look-ahead bias. Prices were transformed into continuously compounded log returns to stabilize variance and remove nonstationarity. Performance was measured with RMSE, MAE, MAPE, sMAPE, MASE, and Theil’s inequality coefficient, while pairwise comparisons relied on the Diebold-Mariano test corrected for small samples using the Harvey-Leybourne-Newbold adjustment. The computational scale was substantial: roughly 2,510 recursive forecasting iterations per currency pair, more than 7,500 cycles and over 30,000 model estimations across three series, all implemented in Python with open-source libraries and a fixed random seed for reproducibility.

The evidence came from both simulation and real markets. In simulations built from a two-regime threshold autoregressive process with 600 observations, ATW-HyF B achieved the lowest forecast errors of all competing models, with an RMSE of 1.0140 and MAE of 0.8075, edging out the standalone ANN and the ATW-HyF A variant. This demonstrated that adaptive weighting combined with volatility modeling is particularly effective when the underlying process exhibits nonlinear and time-varying dynamics, even when volatility clustering is relatively weak.

The empirical results, however, told a more nuanced story. Using daily data from April 2016 to April 2026 with 2,610 observations per series, the study examined three currency pairs: the emerging-market USD/NGN pair and the major pairs EUR/USD and GBP/USD. Descriptive statistics revealed striking differences. USD/NGN returns displayed extreme kurtosis of 115.5 and strong positive skewness, reflecting heavy tails and policy-driven disruptions, while EUR/USD and GBP/USD were comparatively stable yet still non-normal. Jarque-Bera tests rejected normality for all series, and ADF tests confirmed stationarity, while autocorrelation functions dropped quickly to zero, indicating weak serial dependence that makes return prediction inherently difficult.

On these real series, no single model dominated. The ARIMA-ANN hybrid achieved the lowest forecast errors for USD/NGN, with an RMSE of 0.013085, and for EUR/USD, with an RMSE of 0.004809, suggesting that combining linear dynamics with nonlinear learning was sufficient for those markets. ATW-HyF B performed best for GBP/USD, recording the lowest RMSE of 0.006487. Notably, ATW-HyF A and ATW-HyF B produced effectively identical point forecast accuracy on the empirical data, implying that the GARCH volatility layer did not enhance mean forecasts, though it complemented the framework by quantifying forecast uncertainty.

The statistical tests added a twist that elevates the study beyond simple error rankings. Although ARIMA-ANN produced the lowest average forecast errors, the HLN-corrected Diebold-Mariano comparisons showed that ATW-HyF B achieved 18 statistically significant pairwise wins across all currency pairs, while no competing model recorded more than two. ATW-HyF B significantly outperformed the random walk benchmark for all three series, and it beat SETAR everywhere. The distinction between lowest average errors and most consistent statistical superiority highlights why forecast evaluation should combine error-based measures with formal predictive accuracy tests.

The broader lesson is that forecasting performance depends on the characteristics of the underlying exchange-rate series rather than on model complexity alone. Adaptive forecast combination provides a flexible alternative to conventional fixed-weight hybrids, allowing forecasting systems to adjust to changing market conditions, while volatility modeling improves usefulness for forecasting under uncertainty. The authors position the framework as an adaptive benchmark against which computationally intensive deep learning approaches, including LSTM and Transformer architectures, can be evaluated in future work, and recommend extending validation to stock indices, cryptocurrencies, commodity prices, and crisis periods to further establish robustness and generalizability.

Subject of Research: Machine learning and financial forecasting

Article Title: Data-driven adaptive hybrid models for exchange rate return forecasting

Article References: Adesina, O. S., & Obokoh, L. O. (2026). Data-driven adaptive hybrid models for exchange rate return forecasting. Frontiers in Big Data, 9, Article 1917723. https://doi.org/10.3389/fdata.2026.1917723

Image Credits: AI Generated

DOI: 10.3389/fdata.2026.1917723

Keywords: exchange rate forecasting, hybrid models, machine learning, GARCH, ARIMA, neural networks, time series, financial econometrics, Data-driven, adaptive, hybrid, models