Frequency approach for detecting nonstationarity in dependent data

Distinguishing long memory behaviour from nonstationarity can be very difficult as in both cases the sample autocovariance function decays very slowly. Available stationarity tests either do not include long memory or fare poorly in terms of empirical size, especially near the boundary between long memory and nonstationarity. We propose a parameter- free decision rule, that is based on evaluating periodograms at different epochs. We establish some asymptotic theorems in order to validate the method. Limiting distribu- tions are easily tractable as sum of weighted independent χ2 random variables. Moreover, numerical studies are provided to show that the proposed approach outperforms existing methods. We also apply our method to a well-known empirical data, often cited as an example of confusion between long memory and nonstationarity.