Abstract
Consider a multivariate time series where each component series is assumed to be a linear mixture of latent mutually independent stationary time series. Classical independent component analysis (ICA) tools, such as fastICA, are often used to extract latent series, but they don't utilize any information on temporal dependence. Also financial time series often have periods of low and high volatility. In such settings second order source separation methods, such as SOBI, fail. We review here some classical methods used for time series with stochastic volatility, and suggest modifications of them by proposing a family of vSOBI estimators. These estimators use different nonlinearity functions to capture nonlinear autocorrelation of the time series and extract the independent components. Simulation study shows that the proposed method outperforms the existing methods when latent components follow GARCH and SV models. This paper is an invited extended version of the paper presented at the CDAM 2016 conference.
Highlights
In this paper we assume that the observed p-variate time series x =t=0,±1,±2,... follows the basic independent component (IC) model xt = μ + Ωzt, t = 0, ±1, ±2, . . . , where μ is a p-variate location vector, Ω is a full-rank p × p mixing matrix and z =t=0,±1,±2,... is an unobservable p-variate stationary time series such that (i) E(zt) = 0, (ii) COV(zt) = Ip and (iii) the component series of z are independent. x is stationary with E(xt) = μ and COV(xt) = Σ = ΩΩ
The IC model has recently received a lot of attention in financial time series analysis as complicated p-variate time series models can be replaced by p simple univariate (e.g. ARMA or GARCH) models in parameter estimation and prediction problems
We suggested a small modification to existing methods yielding the family of vSOBI estimators
Summary
Is an unobservable p-variate stationary time series such that (i) E(zt) = 0, (ii) COV(zt) = Ip and (iii) the component series of z are independent. In independent component analysis (ICA) the goal is to find, using the observed time series x1, . There exist second order source separation methods, like SOBI (Belouchrani, Abed Meraim, Cardoso, and Moulines 1997), which are popular for analyzing biomedical data Such methods use autocovariances and cross-autocovariances for the estimation. In this paper we review various independent component estimators that use nonlinear autocorrelations, and compare their performance to that of fastICA in a simulation study where independent time series components follow GARCH and SV models.
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