A new Kalman filter approach for the estimation of high-dimensional time-variant multivariate AR models and its application in analysis of laser-evoked brain potentials

Abstract

In this methodological study we present a new version of a Kalman filter technique to estimate high-dimensional time-variant (tv) multivariate autoregressive (tvMVAR) models. It is based on an extension of the state-space model for a multivariate time series to a matrix-state-space model for multi-trial multivariate time series. The result is a general linear Kalman filter (GLKF). The GLKF enables a tvMVAR model estimation which was applied for interaction analysis of simulated data and high-dimensional multi-trial laser-evoked brain potentials (LEP). The tv partial Granger causality index (tvpGCI) was used to investigate the interaction patterns between LEPs derived from an experiment with noxious laser stimulation. First, the new approach was compared with the multi-trial version of the recursive least squares (RLS) algorithm with forgetting factor (Moller et al., 2001) by using 24 distinct electrodes. The RLS failed for a channel number (dimension) higher than 24. Secondly, the analysis was repeated by using all 58 electrodes and the similarities and differences of the GCI-based interaction patterns are discussed. It can be demonstrated that the application of high-dimensional tvMVAR modelling will contribute to a better understanding of the relationship between structure and function.