A Time Series Decomposition Algorithm Based on Gaussian Processes

In this paper, we present an algorithm for decomposing time series based on Gaussian processes. Gaussian processes can be viewed as infinite-dimensional probability distributions over smooth functions and also provide a natural basis for additive decomposition of time series, since we can sum mutually independent Gaussian processes with a simple and elegant algebra involving covariance kernels. The component estimation algorithm we propose in this paper is general and does not depend on the number of components, nor on the correlation structure and interpretation of each component. Specifically, the proposed algorithm is based on nonparametric Bayesian Gaussian process regression, where the log-likelihood covariance is suitably structured to account for the presence of additive subcomponents. The numerical parameter estimation procedure finds MAP estimates by maximizing the unnormalized log-posterior density, with a great advantage in terms of computational cost and efficiency.