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

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 a...

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Bibliographic Details
Published in:Journal of the Royal Statistical Society. Series B, Statistical methodology Statistical methodology, 2009-09, Vol.71 (4), p.831-857
Main Authors: Dette, Holger, Paparoditis, Efstathios
Format: Article
Language:English
Subjects:
Applied statistics
Bootstrap
Bootstrap mechanism
Bootstrap method
Bootstrap resampling
Covariance matrices
Density
Density estimation
Distribution theory
Empirical tests
Estimation
Estimators
Exact sciences and technology
Frequency
General topics
Hypotheses
Inference from stochastic processes
time series analysis
Logical givens
Mathematics
Multiple time series
Multivariate analysis
Non-parametric kernel estimation
Null hypothesis
Parametric inference
Periodogram
Probability and statistics
Sciences and techniques of general use
Spectral densities
Spectral density matrix
Spectral energy distribution
Statistical analysis
Statistical methods
Statistics
Studies
Testing
Time series
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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 Lâ‚‚-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.
ISSN:1369-7412
1467-9868
DOI:10.1111/j.1467-9868.2009.00709.x