On the number of signals in multivariate time series

Abstract

We assume a second-order source separation model where the observed multivariate time series is a linear mixture of latent, temporally uncorrelated time series with some components pure white noise. To avoid the modelling of noise, we extract the non-noise latent components using some standard method, allowing the modelling of the extracted univariate time series individually. An important question is the determination of which of the latent components are of interest in modelling and which can be considered as noise. Bootstrap-based methods have recently been used in determining the latent dimension in various methods of unsupervised and supervised dimension reduction and we propose a set of similar estimation strategies for second-order stationary time series. Simulation studies and a sound wave example are used to show the method's effectiveness.