A test for stationarity based on empirical processes
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Date
2011-09-28
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Abstract
In this paper we investigate the problem of testing the assumption of stationarity in locally stationary processes. The test is based on an estimate of a Kolmogorov-Smirnov-type distance between the true time-varying spectral density and its best approximation through a stationary
spectral density. Convergence of a time-varying empirical spectral process indexed by a class of certain functions is proved and furthermore the consistency of a bootstrap procedure is shown, which is used to approximate the limiting distribution of the test statistic. Compared to other
methods proposed in the literature for the problem of testing for stationarity the new approach has at least two advantages. On the one hand the test can detect local alternatives converging to the
null hypothesis at a rate 1/sqrt(T) (where T denotes the sample size). On the other hand the method
only requires the specification of one regularization parameter. The finite sample properties of the
method are investigated by means of a simulation study and a comparison with two other tests is
provided which have been proposed in the literature for testing stationarity.
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Keywords
spectral density, bootstrap, locally stationary process, integrated periodogram, empirical spectral measure, goodness-of-fit tests, non-stationary processes