Time series forecasting with Gaussian Processes needs priors
This work addresses the lack of competitive automatic forecasting methods using Gaussian Processes for practitioners in time series analysis, though it is incremental as it builds on existing GP techniques.
The authors tackled the problem of automatic time series forecasting with Gaussian Processes by proposing a fixed kernel composition with automatic relevance determination and empirical Bayes priors for hyperparameters, resulting in a model that is more accurate than state-of-the-art methods and fast to train with a single restart.
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.