Non-parametric Probabilistic Time Series Forecasting via Innovations Representation

TL;DR

This paper introduces a nonparametric probabilistic time series forecasting method based on innovations representation, leveraging deep learning and Monte Carlo sampling to improve predictive accuracy over existing benchmarks.

Contribution

It develops a novel deep-learning approach that circumvents the need for known distributions and causal decoders in innovations-based time series modeling.

Findings

Marked improvement over benchmarks in electricity price forecasting

Effective modeling of conditional probability distributions

Demonstrates robustness across diverse datasets

Abstract

Probabilistic time series forecasting predicts the conditional probability distributions of the time series at a future time given past realizations. Such techniques are critical in risk-based decision-making and planning under uncertainties. Existing approaches are primarily based on parametric or semi-parametric time-series models that are restrictive, difficult to validate, and challenging to adapt to varying conditions. This paper proposes a nonparametric method based on the classic notion of {\em innovations} pioneered by Norbert Wiener and Gopinath Kallianpur that causally transforms a nonparametric random process to an independent and identical uniformly distributed {\em innovations process}. We present a machine-learning architecture and a learning algorithm that circumvent two limitations of the original Wiener-Kallianpur innovations representation: (i) the need for known probability distributions of the time series and (ii) the existence of a causal decoder that reproduces the original time series from the innovations representation. We develop a deep-learning approach and a Monte Carlo sampling technique to obtain a generative model for the predicted conditional probability distribution of the time series based on a weak notion of Wiener-Kallianpur innovations representation. The efficacy of the proposed probabilistic forecasting technique is demonstrated on a variety of electricity price datasets, showing marked improvement over leading benchmarks of probabilistic forecasting techniques.