A nonparametric test for slowly-varying nonstationarities

This paper develops a new nonparametric method that is suitable for detecting slowly-varying nonstationarities that can be seen as trends in the time marginal of the time-varying spectrum of the signal. The rationale behind the proposed method is to measure the importance of the trend in the time marginal by using a proper test statistic, and further compare this measurement with the ones that are likely to be found in stationary references. It is shown that the distribution of the test statistic under stationarity can be modeled fairly well by a Generalized Extreme Value (GEV) pdf, from which a threshold can be derived for testing stationarity by means of a hypothesis test. Finally, the new method is compared with other ones found in the literature.