Robust testing for stationarity in the presence of outliers

Testing the stationarity of stochastic processes is required in a variety of signal processing applications. When dealing with real-world problems, the presence of outliers and impulsive (heavy-tailed) noise causes classical stationarity tests to break down. In this work, a set of robust stationarity tests that are based on a sphericity statistic test (SST) in the frequency domain is proposed. Different possible approaches are investigated and compared to existing robust and non-robust stationarity tests in terms of the receiver operating characteristic (ROC). In addition to extensive simulations, a real-world data example of a malfunctioning window regulator motor, for which the dominant frequencies show a modulating character that results in a non-stationary signal, is investigated. Both for simulated and real-world data, the proposed methods significantly outperform existing approaches.