Title: Estimation of the long run variance in case of multiple level shifts
Authors: Sheila Goerz - TU Dortmund (Germany) [presenting]
Alexander Duerre - TU Dortmund (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. We propose a new kernel-type estimator for the long run variance. It is based on the sum of weighted autocovariances. The classical kernel or Bartlett estimator uses a weighted sum of autocovariances giving larger time lags smaller weights. We substitute autocovariance estimations which are especially suitable under change points for the common used empirical autocovariances. To be robust against level shifts we use a rolling window to estimate the location instead of the global mean. Depending on the window size the resulting estimator is highly biased. Therefore a correction is applied. In a simulation study we compare our estimator with commonly used ones.