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 L 2 -distance measure between the nonpara- metrically 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 as- ymptotic 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. Primary 62M10, 62M15; secondary 62G09