  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.
