Permutation principles for the change analysis of stochastic processes under strong invariance

Approximations of the critical values for change-point tests are obtained through permutation methods. Both, abrupt and gradual changes are studied in models of possibly dependent observations satisfying a strong invariance principle, as well as gradual changes in an i.i.d. model. The theoretical results show that the original test statistics and their corresponding permutation counterparts follow the same distributional asymptotics. Some simulation studies illustrate that the permutation tests behave better than the original tests if performance is measured by the α - and β -error, respectively.