Abstract: A restrictive assumption in change point analysis is “stationarity under the null hypothesis of no change-point”, which is crucial for asymptotic theory but not very realistic from a practical point of view. For example, if change point analysis for correlations is performed, it is not necessarily clear that the mean, marginal variance or higher order moments are constant, even if there is no change in the correlation. This paper develops change point analysis for the correlation structures under less restrictive assumptions. In contrast to previous work, our approach does not require that the mean, variance and fourth order joint cumulants are constant under the null hypothesis. Moreover, we also address the problem of detecting relevant change points.

Key words and phrases: Change point analysis, local linear estimation, piecewise locally stationary process, relevant change points, second order structure.