Abstract

Regression using Gaussian process models is applied to time-series data analysis. To extract from the data separate components with different frequency scales, the Gaussian regression methodology is extended through the use of multiple Gaussian process models. Fast and memory-efficient methods, as required by Gaussian regression to cater for large time-series data sets, are discussed. These methods are based on the generalised Schur algorithm and a procedure to determine the Schur decomposition of matrices, the key step to realising them, is presented. In addition, a procedure to appropriately initialise the Gaussian process model training is presented. The utility of the procedures is illustrated by application of a multiple Gaussian process model to extract separate components with different frequency scales from a 5000-point time-series data set with gaps.