Neural ARFIMA model for forecasting BRIC exchange rates with long memory under oil shocks and policy uncertainties

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, nonlinearity, and non-stationarity properties that conventional time series models struggle to capture. Additionally, there exist several key drivers of exchange rate dynamics, including global economic policy uncertainty, US equity market volatility, US monetary policy uncertainty, oil price growth rates, and country-specific short-term interest rate differentials. These empirical complexities underscore the need for a flexible modeling framework that can jointly accommodate long memory, nonlinearity, and the influence of external drivers. To address these challenges, we propose a Neural AutoRegressive Fractionally Integrated Moving Average (NARFIMA) model that combines the long-memory representation of ARFIMA with the nonlinear learning capacity of neural networks, while flexibly incorporating exogenous causal variables. We establish theoretical properties of the model, including asymptotic stationarity of the NARFIMA process using Markov chains and nonlinear time series techniques. We quantify forecast uncertainty using conformal prediction intervals within the NARFIMA framework. Empirical results across six forecast horizons show that NARFIMA consistently outperforms various state-of-the-art statistical and machine learning models in forecasting BRIC exchange rates. These findings provide new insights for policymakers and market participants navigating volatile financial conditions. The \texttt{narfima} \textbf{R} package provides an implementation of our approach.