Functional CLT for nonparametric estimates of the spectrum and change- point problem for a spectral function. (English. Russian original) Zbl 0761.62123

Lith. Math. J. 30, No. 4, 302-322 (1990); translation from Lit. Mat. Sb. 30, No. 4, 674-697 (1990).
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 D. Picard [Adv. Appl. Probab. 17, 841- 867 (1985; Zbl 0585.62151)] relating to the case of a Gaussian sequence.


62M15 Inference from stochastic processes and spectral analysis
62G07 Density estimation
60F17 Functional limit theorems; invariance principles


Zbl 0585.62151
Full Text: DOI


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