Tests for comparing time‐invariant and time‐varying spectra based on the Anderson–Darling statistic

Based on periodogram-ratios of two univariate time series at different frequency points, two tests are proposed for comparing their spectra. One is an Anderson-Darling-like statistic for testing the equality of two time-invariant spectra. The other is the maximum of Anderson-Darling-like statistics for testing the equality of two spectra no matter that they are time-invariant and time-varying. Both of two tests are applicable for independent or dependent time series. Several simulation examples show that the proposed statistics outperform those that are also based on periodogram-ratios but constructed by the Pearson-like statistics.