Testing For Equality Of Spectral Densities Of Stationary Time Series

Testing for equality of components of the stationary time series is an im-portant issue in time series analysis. In recent years, testing for equality of components of the stationary time series is mainly conducted in the frequency domain, which is based on the spectral density and its estimators periodogram to construct test statistics. We also consider the problem in the frequency domain and give two methods of testing for equality of components of the stationary time series by means of the correlation property of the spectral density and the periodogram.The first method is mainly based on the assumption of the two spectral densities are equal and the quotient of the two periodogram of time series obeys the F(2,2) distribution. According to the periodogram of two time series, we constructed a test statistics that test whether the two spectral density is equal and obey asymptotic normality.The second method is that according to Dette et al. method which testing whether the spectral density of the two time series is equal. We give a weighting method under L2 distance that inherits the large sample properties of Dette et al. Test statistic have prosperities of asymptotic normality.The simulation shows that the first method proposed statistic is superior than that of Dette et al. in the aspect of empirical powers for independent sta-tionary time series, and the second method proposed statistic is superior than that of Dette et al. in the aspect of empirical powers for general stationary time series. It is obviously showed that the proposed statistic is more effective than that of Dette et al. when we testing for equality of spectral densities of 8 com-ponents of the series of the Fmri blood oxidizing level signals.