On the number of signals in multivariate time series

TL;DR

This paper introduces bootstrap-based methods to determine the number of meaningful signals in multivariate time series, enabling better separation of noise and signal components for improved modeling.

Contribution

It proposes novel bootstrap-based estimation strategies for identifying the number of non-noise latent components in second-order stationary multivariate time series.

Findings

Methods effectively distinguish signal from noise in simulations

Application to sound wave data demonstrates practical utility

Bootstrap approaches outperform traditional criteria in accuracy

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.