Time series forecasting with Gaussian Processes needs priors

TL;DR

This paper introduces a Gaussian Process-based approach for automatic time series forecasting, focusing on kernel selection and hyperparameter estimation using priors, resulting in improved accuracy and efficiency.

Contribution

It proposes a fixed kernel composition with automatic relevance determination and empirical Bayes priors for hyperparameters, enhancing automatic forecasting with GPs.

Findings

GP model outperforms state-of-the-art methods

Single restart suffices for hyperparameter estimation

Model achieves high accuracy across diverse time series

Abstract

Automatic forecasting is the task of receiving a time series and returning a forecast for the next time steps without any human intervention. Gaussian Processes (GPs) are a powerful tool for modeling time series, but so far there are no competitive approaches for automatic forecasting based on GPs. We propose practical solutions to two problems: automatic selection of the optimal kernel and reliable estimation of the hyperparameters. We propose a fixed composition of kernels, which contains the components needed to model most time series: linear trend, periodic patterns, and other flexible kernel for modeling the non-linear trend. Not all components are necessary to model each time series; during training the unnecessary components are automatically made irrelevant via automatic relevance determination (ARD). We moreover assign priors to the hyperparameters, in order to keep the inference within a plausible range; we design such priors through an empirical Bayes approach. We present results on many time series of different types; our GP model is more accurate than state-of-the-art time series models. Thanks to the priors, a single restart is enough the estimate the hyperparameters; hence the model is also fast to train.