We propose a frequency domain generalized likelihood ratio test for testing nonstationarity in time series. The test is constructed in the frequency domain by comparing the goodness of fit in the log-periodogram regression under the varying coefficient fractionally exponential models. Under such a locally stationary specification, the proposed test is capable of detecting dynamic changes of short-range and long-range dependences in a regression framework. The asymptotic distribution of the proposed test statistic is known under the null stationarity hypothesis, and its finite sample distribution can be approximated by bootstrap. Numerical results show that the proposed test has good power against a wide range of locally stationary alternatives. 
A frequency domain test for detecting nonstationary time series