Multi-Horizon Time Series Forecasting of Non-Parametric CDFs with Deep Lattice Networks

Abstract

Probabilistic forecasting is not only a way to add more information to a prediction of the future, but it also builds on weaknesses in point prediction. Sudden changes in a time series can still be captured by a cumulative distribution function (CDF), while a point prediction is likely to miss it entirely. The modeling of CDFs within forecasts has historically been limited to parametric approaches, but due to recent advances, this no longer has to be the case. We aim to advance the fields of probabilistic forecasting and monotonic networks by connecting them and propose an approach that permits the forecasting of implicit, complete, and nonparametric CDFs. For this purpose, we propose an adaptation to deep lattice networks (DLN) for monotonically constrained simultaneous/implicit quantile regression in time series forecasting. Quantile regression usually produces quantile crossovers, which need to be prevented to achieve a legitimate CDF. By leveraging long short term memory units (LSTM) as the embedding layer, and spreading quantile inputs to all sub-lattices of a DLN with an extended output size, we can produce a multi-horizon forecast of an implicit CDF due to the monotonic constraintability of DLNs that prevent quantile crossovers. We compare and evaluate our approach