Neural ARFIMA model for forecasting BRIC exchange rates with long memory

arXiv:2509.06697v2 Announce Type: replace-cross Abstract: Accurate forecasting of exchange rates remains a persistent challenge, particularly for emerging economies such as Brazil, Russia, India, and China (BRIC). These series exhibit long memory and nonlinearity that conventional time series models struggle to capture. Exchange rate dynamics are further influenced by several key drivers, including global economic policy uncertainty, US equity market volatility, US monetary policy uncertainty, oil price growth rates, and short-term interest rates. These empirical complexities underscore the need for a flexible framework that can jointly accommodate long memory, nonlinearity, and the influence of external drivers. We propose a Neural AutoRegressive Fractionally Integrated Moving Average (NARFIMA) model that combines the long memory structure of ARFIMA with the nonlinear learning capability of neural networks while incorporating exogenous variables. We establish asymptotic stationarity of NARFIMA and quantify forecast uncertainty using conformal prediction intervals. Empirical results show that NARFIMA consistently outperforms benchmark methods in forecasting BRIC exchange rates.