Bootstrapping frequency domain tests in multivariate time series with an applicaton to comparing spectral densities
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Date
2009-01-13T07:50:26Z
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Abstract
We propose a general bootstrap procedure to approximate the null distribution of nonparametric 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 proposed bootstrap procedure. We apply a version of this procedure together with a new statistic in order to test the hypothesis that the spectral densities of not necessarily independent time series are equal. The test statistic proposed is based on a L2-distance between the nonparametrically estimated individual spectral densities and an overall, 'pooled' spectral density, the later being obtained using the whole set
of m time series considered. The effects of the dependence between the time series on
the power behavior of the test are investigated. Some simulations are presented and a real-life data example is discussed.
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Keywords
Bootstrap, Multiple time series, Nonparametric kernel estimation, Periodogram, Spectral density matrix