Testing equality of spectral densities
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Date
2007-10-25T12:00:40Z
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Abstract
We develop a test of the hypothesis that the spectral densities of a
number m, m ≥ 2, not necessarily independent time series are equal. The test
proposed is based on an appropriate L 2
-distance measure between the nonpara-
metrically estimated individual spectral densities and an overall, ’pooled’ spectral
density, the later being obtained using the whole set of m time series considered.
The limiting distribution of the test statistic under the null hypothesis of equal
spectral densities is derived and a novel frequency domain bootstrap method is
presented in order to approximate more accurately this distribution. The as-
ymptotic distribution of the test and its power properties for fixed alternatives
are investigated. Some simulations are presented and a real-life data example is
discussed.
Primary 62M10, 62M15; secondary 62G09
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Keywords
Bootstrap, Multiple time series, Nonparametric kernel, Periodogram, Spectral density matrix