Title: Comparison of different estimators of the long run variance for the cusum test
Authors: Julia Duda - TU Dortmund (Germany) [presenting]
Alexander Duerre - TU Dortmund (Germany)
Roland Fried - TU Dortmund University (Germany)
Abstract: The cusum test is one of the most popular tools in change-point detection. Under short range dependence and fairly mild technical conditions cusum type tests depend only on one nuisance parameter, often called long run variance, but apart from that, they are distribution free. There are many proposals to estimate the long run variance non-parametrically which are all challenged by simultaneously being unbiased under the null hypothesis and giving reasonable results under the alternative. If one does not account for a possible change-point, estimators of the long run variance get inflated in case of a level shift yielding a considerable loss in power. On the other hand, accounting for a change-point often leads to a conspicuous bias in small samples resulting in substantially anti-conservative tests. We review and compare different proposals to estimate the long run variance, mainly concentrating on the two most popular approaches: kernel and bootstrap estimators. An extensive simulation study also reveals suitable tuning parameters of the presented procedures.