An asymptotic test on the stationarity of the variance

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.