Probabilistic AutoRegressive Neural Networks for Accurate Long-range Forecasting

TL;DR

The paper introduces PARNN, a hybrid probabilistic neural network model that improves long-range time series forecasting by combining classical ARIMA feedback with neural networks, providing superior accuracy and uncertainty quantification.

Contribution

It presents the novel PARNN model that integrates ARIMA feedback into autoregressive neural networks, enhancing forecasting accuracy and interpretability for complex time series.

Findings

PARNN outperforms standard statistical and deep learning models across various datasets.

The model provides reliable uncertainty quantification through prediction intervals.

PARNN demonstrates superior long-range forecasting accuracy in diverse real-world applications.

Abstract

Forecasting time series data is a critical area of research with applications spanning from stock prices to early epidemic prediction. While numerous statistical and machine learning methods have been proposed, real-life prediction problems often require hybrid solutions that bridge classical forecasting approaches and modern neural network models. In this study, we introduce the Probabilistic AutoRegressive Neural Networks (PARNN), capable of handling complex time series data exhibiting non-stationarity, nonlinearity, non-seasonality, long-range dependence, and chaotic patterns. PARNN is constructed by improving autoregressive neural networks (ARNN) using autoregressive integrated moving average (ARIMA) feedback error, combining the explainability, scalability, and "white-box-like" prediction behavior of both models. Notably, the PARNN model provides uncertainty quantification through prediction intervals, setting it apart from advanced deep learning tools. Through comprehensive computational experiments, we evaluate the performance of PARNN against standard statistical, machine learning, and deep learning models, including Transformers, NBeats, and DeepAR. Diverse real-world datasets from macroeconomics, tourism, epidemiology, and other domains are employed for short-term, medium-term, and long-term forecasting evaluations. Our results demonstrate the superiority of PARNN across various forecast horizons, surpassing the state-of-the-art forecasters. The proposed PARNN model offers a valuable hybrid solution for accurate long-range forecasting. By effectively capturing the complexities present in time series data, it outperforms existing methods in terms of accuracy and reliability. The ability to quantify uncertainty through prediction intervals further enhances the model's usefulness in decision-making processes.