State Space Approximation of Gaussian Processes for Time Series Forecasting

Gaussian Processes (GPs), with a complex enough additive kernel, provide competitive results in time series forecasting compared to state-of-the-art approaches (arima, ETS) provided that: (i) during training the unnecessary components of the kernel are made irrelevant by automatic relevance determination; (ii) priors are assigned to each hyperparameter. However, GPs computational complexity grows cubically in time and quadratically in memory with the number of observations. The state space (SS) approximation of GPs allows to compute GPs based inferences with linear complexity. In this paper, we apply the SS representation to time series forecasting showing that SS models provide a performance comparable with that of full GP and better than state-of-the-art models (arima, ETS). Moreover, the SS representation allows us to derive new models by, for instance, combining ETS with kernels.