Resampling in the frequency domain of time series to determine critical values for change-point tests

Summary We study a model with an abrupt change in the mean and dependent errors that form a linear process. Different kinds of statistics are considered, such as maximum-type statistics (particularly different CUSUM procedures) or sum-type statistics. Approximations of the critical values for change-point tests are obtained through permutation methods in the frequency domain. The theoretical results show that the original test statistics and their corresponding frequency permutation counterparts follow the same distributional asymptotics. The main step in the proof is to obtain limit theorems for the corresponding rank statistics and then deduce the permutation asymptotics conditionally on the given data. Some simulation studies illustrate that the permutation tests usually behave better than the original tests if performance is measured by the α- and β-errors respectively.