Prediction Interval Construction for Multivariate Point Forecasts Using Deep Learning

It has been demonstrated that deep learning can in certain instances outperform traditional statistical methods at forecasting. This outperformance, however, does not address the challenge of quantifying forecast uncertainty (prediction intervals). Artificial neural networks often do not have probability distributions linked to their point forecasts, which complicates the construction of prediction intervals. In this paper, we explore computational methods of artificially deriving said probability distributions and constructing prediction intervals. The point forecasts, and the associated constructed prediction intervals are compared to those produced by means of the oft-preferred traditional statistical counterparts. Our finding is deep learning outperforms (or at the very least is competitive to) the former. We focus on three deep learning architectures, namely, cascaded neural networks, reservoir computing and long short-term memory recurrent neural networks.