# Neural ARFIMA model for forecasting BRIC exchange rates with long memory

arXiv: https://arxiv.org/abs/2509.06697 · HTML: https://mlsanity.com/paper/2509.06697/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 92 references that are in the map.
- First posted on arXiv 8 Sep 2025.

## Builds on (most cited first, 9 of 9)

- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [TSMixer: An All-MLP Architecture for Time Series Forecasting](https://mlsanity.com/paper/2303.06053/) (2023)
- [Do RNN and LSTM have Long Memory?](https://mlsanity.com/paper/2006.03860/) (2020)
- [Of Quantiles and Expectiles: Consistent Scoring Functions, Choquet Representations, and Forecast Rankings](https://mlsanity.com/paper/1503.08195/) (2015)
- [Epicasting: An Ensemble Wavelet Neural Network (EWNet) for Forecasting Epidemics](https://mlsanity.com/paper/2206.10696/) (2022)
- [Macroeconomic Predictions using Payments Data and Machine Learning](https://mlsanity.com/paper/2209.00948/) (2022)
- [A nonlinearity and model specification test for functional time series](https://mlsanity.com/paper/2304.01558/) (2023)

## Abstract (arXiv)

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.