Multi-scale test procedure for non-stationarity in short and long memory time series

In this paper, we develop a test procedure for non-stationarity for possibly long-memory processes. Contrary to most of the proposed methods, the test procedure has the same distribution for short-range and long-range dependence stationary processes. Such tests have been already proposed in [1], but these authors do not have taken into account the dependence of the wavelet coefficients within scales and between scales. We also propose an application to electric power consumption monitoring.