Functional CLT for nonparametric estimates of the spectrum and change-point problem for a spectral function

Abstract

SUMMARY We prove the c.l.t. (on convergence in the Skorokhod space of two-parameter functions) for spectral statistics analogous to statistics of Kolmogorov-Smirnov type connected with the change-point of the spectrum of a stationary moving average sequence. The paper generalizes and supplements the results of Picard [28] relating to the case of a Gaussian sequence.