The comparision of two spectral density functions using the bootstrap

Abstract

Let {X n } and {Y n } be two stationary and ergodic processes with power spectral density functions P x (f) and Px (f) respectively. The problem considered is that of deriving nonparametric tests for the null-hypothesis for all Three test statistics are used, viz. a Kolmogorov-Smirnov type statistic, a X 2-statistic and a Kullback-Leibler type statistic. The bootstrap method is applied to obtain critical values and to compare the power functions of these test procedures. The results of some Monte Carlo studies, which illustrate the performance of the various procedures, are also given.