Detecting Relevant Changes in Time Series Models

Dominik Wied (TU Dortmund)
Wednesday, October 22, 2014 - 10:00am
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

Most of the literature on change-point analysis by means of hypothesis testing considers null hypotheses in which a certain parameter is constant over time. This presentation takes a different perspective and investigate the null hypotheses of no relevant changes. Here, the difference between the parameter before and after a change point is smaller than a positive threshold. This formulation of the testing problem is motivated by the fact that in many applications a modification of the statistical analysis might not be necessary, if the difference between the parameters before and after the change-point is small. Moreover, the framework allows for constructing confidence intervals. A general approach to problems of this type is developed which is based on the CUSUM principle. For the asymptotic analysis weak convergence of the sequential empirical process has to be established under the alternative of non-stationarity and it is shown that the resulting test statistic is asymptotically normal distributed. Several applications of the methodology are given including tests for relevant changes in the mean, parameter in a linear regression model and distribution function. The finite sample properties of the new tests are investigated by means of a simulation study and illustrated by analyzing a data example from economics.