An asymptotic test on the stationarity of the variance
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Date
2016
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Abstract
We reconsider a statistic introduced in Wornowizki et al. (2016) allowing to
test the stationarity of the variance for a sequence of independent random variables. In-
stead of determining rejection regions via the permutation principle as proposed before, we
provide asymptotic critical values leading to huge savings in computation time. To prove
the required limit theorems, the test statistic is viewed as a U-statistic constructed from
blockwise variance estimates. Since the distribution of the test statistic depends on the
sample size, a suitable new law of large numbers as well as a central limit theorem are
developed. These asymptotic results are illustrated on artificial data. The permutation and
asymptotic version of the test are compared to alternative procedures in extensive Monte
Carlo experiments. The simulation results suggest that the methods offer similar results
and high power when compared to their competitors, particularly in the case of multiple
structural breaks. They also estimate the structural break positions adequately.
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Keywords
change point analysis, piecewise identical distribution and U-statistic, variance