An Interpretable Probabilistic Autoregressive Neural Network Model for Time Series Forecasting
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Forecasting time series data presents an emerging field of data science that has its application ranging from stock price and exchange rate 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 generating 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, and therefore, hybrid solutions are needed to bridge the gap between classical forecasting methods and scalable neural network models. We introduce an interpretable probabilistic autoregressive neural network model for an explainable, scalable, and "white box-like" framework that can handle a wide variety of irregular time series data (e.g., nonlinearity and nonstationarity). Sufficient conditions for asymptotic stationarity and geometric ergodicity are obtained by considering the asymptotic behavior of the associated Markov chain. During computational experiments, PARNN outperforms standard statistical, machine learning, and deep learning models on a diverse collection of real-world datasets coming from economics, finance, and epidemiology, to mention a few. Furthermore, the proposed PARNN model improves forecast accuracy significantly for 10 out of 12 datasets compared to state-of-the-art models for short to long-term forecasts.
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