PARNN: A Probabilistic Autoregressive Neural Network Framework for Accurate Forecasting

Forecasting time series data represents an emerging field of research in data science and knowledge discovery with vast applications ranging from stock price and energy demand prediction to the early prediction of epidemics. Numerous statistical and machine learning methods have been proposed in the last five decades with the demand for high-quality and reliable forecasts. However, in real-life prediction problems, situations exist in which a model based on one of the above paradigms is preferable. Therefore, hybrid solutions are needed to bridge the gap between classical forecasting methods and modern neural network models. In this context, we introduce a Probabilistic AutoRegressive Neural Network (PARNN) model that can handle a wide variety of complex time series data (e.g., nonlinearity, non-seasonal, long-range dependence, and non-stationarity). The proposed PARNN model is built by creating a fusion of an integrated moving average and autoregressive neural network to preserve the explainability, scalability, and "white-boxlike" prediction behavior of the individuals. Sufficient conditions for asymptotic stationarity and geometric ergodicity are obtained by considering the asymptotic behavior of the associated Markov chain. Unlike advanced deep learning tools, the uncertainty quantification of the PARNN model based on prediction intervals is obtained. During computational experiments, PARNN outperforms standard statistical, machine learning, and deep learning models (e.g., Transformers, NBeats, DeepAR, etc.) on a diverse collection of real-world datasets from macroeconomics, tourism, energy, epidemiology, and others for short-term, medium-term, and long-term forecasting. Multiple comparisons with the best method are carried out to showcase the superiority of the proposal in comparison with the state-ofthe-art forecasters over different forecast horizons.