Bootstrapping frequency domain tests in multivariate time series with an application to comparing spectral densities

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2009 · Volume 71 · Issue 4

DOI: 10.1111/j.1467-9868.2009.00709.x

Abstract

Summary.We propose a general bootstrap procedure to approximate the null distribution of non-parametric frequency domain tests about the spectral density matrix of a multivariate time series. Under a set of easy-to-verify conditions, we establish asymptotic validity of the bootstrap procedure proposed. We apply a version of this procedure together with a new statistic to test the hypothesis that the spectral densities of not necessarily independent time series are equal. The test statistic proposed is based on anL2-distance between the non-parametrically estimated individual spectral densities and an overall, ‘pooled’ spectral density, the latter being obtained by using the whole set ofmtime series considered. The effects of the dependence between the time series on the power behaviour of the test are investigated. Some simulations are presented and a real life data example is discussed.

Keywords

Bootstrap, Multiple time series, Non-parametric kernel estimation, Periodogram, Spectral density matrix

Enable JavaScript for citation tools and additional paper interactions.