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In this paper we introduce a novel online time series forecasting model werefer to as the pM-GP filter. We show that our model is equivalent to Gaussianprocess regression, with the advantage that both online forecasting and onlinelearning of the hyper-parameters have a constant (rather than cubic) timecomplexity and a constant (rather than squared) memory requirement in thenumber of observations, without resorting to approximations. Moreover, theproposed model is expressive in that the family of covariance functions of theimplied latent process, namely the spectral Matern kernels, have recently beenproven to be capable of approximating arbitrarily well anytranslation-invariant covariance function. The benefit of our approach comparedto competing models is demonstrated using experiments on several real-lifedatasets.

p-Markov Gaussian Processes for Scalable and Expressive Online Bayesian Nonparametric Time Series Forecasting