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

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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 an L2-distance between the non-parametrically estimated individual spectral densities and an overall, ‘pooled’ spectral density, the latter being obtained by using the whole set of m time 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

Document Type: Research Article

DOI: https://doi.org/10.1111/j.1467-9868.2009.00709.x

Affiliations: 1: Ruhr-Universit├Ąt Bochum, Germany 2: University of Cyprus, Nicosia, Cyprus

Publication date: 2009-09-01

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