  In this paper we introduce a novel online time series forecasting model we
refer to as the pM-GP filter. We show that our model is equivalent to Gaussian
process regression, with the advantage that both online forecasting and online
learning of the hyper-parameters have a constant (rather than cubic) time
complexity and a constant (rather than squared) memory requirement in the
number of observations, without resorting to approximations. Moreover, the
proposed model is expressive in that the family of covariance functions of the
implied latent process, namely the spectral Matern kernels, have recently been
proven to be capable of approximating arbitrarily well any
translation-invariant covariance function. The benefit of our approach compared
to competing models is demonstrated using experiments on several real-life
datasets.
