Testing equality of spectral densities

Abstract

We develop a test of the hypothesis that the spectral densities of a number m, m ≥ 2, not necessarily independent time series are equal. The test proposed is based on an appropriate L2-distance measure between the nonparametrically estimated individual spectral densities and an overall, ’pooled’ spectral density, the later being obtained using the whole set of m time series considered. The limiting distribution of the test statistic under the null hypothesis of equal spectral densities is derived and a novel frequency domain bootstrap method is presented in order to approximate more accurately this distribution. The asymptotic distribution of the test and its power properties for fixed alternatives are investigated. Some simulations are presented and a real-life data example is discussed.