Exchange rate forecasting remains a challenging problem, particularly for emerging economies, where the observed time series exhibit pronounced long-memory dependence, nonlinear dynamics, and sensitivity to macro-financial drivers. Classical models such as ARFIMA capture long-range persistence but fail to adequately represent nonlinear relationships, while modern machine learning approaches often neglect the underlying long-memory structure in macroeconomic series. To address this gap, we propose a Neural AutoRegressive Fractionally Integrated Moving Average (NARFIMA) model that integrates ARFIMA-based long-memory modeling with neural networks for nonlinear function approximation, while incorporating exogenous macroeconomic and uncertainty indicators. The framework provides a unified approach for capturing persistence, nonlinear dynamics, and external shocks. We establish asymptotic stationarity of the NARFIMA process and develop conformal prediction intervals for distribution-free uncertainty quantification. Empirical results for BRIC exchange rates show that NARFIMA consistently outperforms a broad range of forecasting benchmarks across multiple horizons, underscoring the importance of explicitly modeling long-memory dependence in exchange rate dynamics. The `narfima' R package provides an implementation of our approach.

翻译：汇率预测仍是一个具有挑战性的问题，尤其对于新兴经济体而言，其观测时间序列表现出显著的长记忆依赖性、非线性动态特征以及对宏观金融驱动因素的敏感性。ARFIMA等经典模型虽能捕捉长程持续性，却难以充分表征非线性关系；而现代机器学习方法往往忽视宏观经济序列中潜在的长记忆结构。为弥补这一空白，我们提出神经自回归分数积分移动平均（NARFIMA）模型，该模型将基于ARFIMA的长记忆建模与用于非线性函数逼近的神经网络相结合，同时纳入外生宏观经济与不确定性指标。该框架为捕捉持续性、非线性动态及外部冲击提供了统一方法。我们建立了NARFIMA过程的渐近平稳性，并开发了适用于分布自由不确定性量化的保形预测区间。针对金砖国家汇率开展的实证研究表明，NARFIMA在多个预测时域上持续优于一系列基准预测模型，凸显了在汇率动态中显式建模长记忆依赖性的关键作用。narfima R语言包提供了该方法的实现。