Abstract
Multivariate time series observations are increasingly common in multiple fields of science but the complex dependencies of such data often translate into intractable models with large number of parameters. An alternative is given by first reducing the dimension of the series and then modelling the resulting uncorrelated signals univariately, avoiding the need for any covariance parameters. A popular and effective framework for this is blind source separation. In this paper we review the dimension reduction tools for time series available in the R package tsBSS. These include methods for estimating the signal dimension of second-order stationary time series, dimension reduction techniques for stochastic volatility models and supervised dimension reduction tools for time series regression. Several examples are provided to illustrate the functionality of the package.
Highlights
In many fields of applied science multivariate time series, xt =, t = 1, . . . T, are collected
One commonly used noisy blind source separation (BSS) model is the one where an additive external noise vector is included in model (1), that is, we assume that xt = μ + Ωzt + t, t = 0, ±1, ±2, . . . , where t ∈ Rp is a vector of white noise (Comon and Jutten 2010)
The drawback of the AMUSE procedure is that, in order to separate all p source components, we need to assume that for a chosen lag τ, the eigenvalues in Λτ are distinct. As this may not hold in practice, it is often better to use approximate joint diagonalization of several autocovariance matrices as suggested in Belouchrani et al (1997). Their SOBI method is a natural extension of AMUSE as the solution is given by W = U Cov(xt)−1/2 where the orthogonal U = (u1, . . . , up) ∈ Rp×p maximizes p (ui Covτui)2, τ ∈T i=1 that is, we find a rotation that makes the autocovariance matrices defined by a set of lags T = {τ1, . . . , τK} “as diagonal as possible”
Summary
Consider current biomedical datasets where the number of time series components vary from hundreds to millions, and the main aim of the analysis is to separate the signals of interest from noise. For such high-dimensional data, fitting multivariate time series models might become impossible, and at the very least unreasonable as it is not sensible to assign a huge number of model parameters for noise components. In this paper we illustrate how blind source separation (BSS) methods (see for example Comon and Jutten 2010; Nordhausen and Oja 2018) can be used for dimension reduction in a time series context. The package tsBSS is available from the Comprehensive R Archive Network (CRAN) at https://CRAN.R-project.org/package=tsBSS
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
