Wavelet based time-varying vector autoregressive modelling

Authors:
João R. Sato;Pedro A. Morettin;Paula R. Arantes;Edson Amaro, Jr.
Affiliations:
Institute of Mathematics and Statistics, University of São Paulo, Rua do Matão, 1010, 05508-090, São Paulo, Brazil and NIF: Functional Neuroimage Research, University of São Pa ...;Institute of Mathematics and Statistics, University of São Paulo, Rua do Matão, 1010, 05508-090, São Paulo, Brazil;Department of Radiology, Medical School, University of São Paulo, Brazil and NIF: Functional Neuroimage Research, University of São Paulo, Brazil;Department of Radiology, Medical School, University of São Paulo, Brazil and NIF: Functional Neuroimage Research, University of São Paulo, Brazil
Venue:
Computational Statistics & Data Analysis
Year:
2007

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Abstract

Vector autoregressive (VAR) modelling is one of the most popular approaches in multivariate time series analysis. The parameters interpretation is simple, and provide an intuitive identification of relationships and Granger causality among time series. However, the VAR modelling requires stationarity conditions which could not be valid in many practical applications. Locally stationary or time dependent modelling seem attractive generalizations, and several univariate approaches have already been proposed. In this paper we propose an estimation procedure for time-varying vector autoregressive processes, based on wavelet expansions of autoregressive coefficients. The asymptotic properties of the estimator are derived and illustrated by computer intensive simulations. We also present an application to brain connectivity identification using functional magnetic resonance imaging (fMRI) data sets.