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On asymptotic normality of estimates for correlation functions of stationary Gaussian processes in the space of continuous functions

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Abstract

We establish conditions of the weak convergence of the empirical correlogram of a stationary Gaussian process to some Gaussian process in the space of continuous functions. We prove that such a convergence holds for a broad class of stationary Gaussian processes with square integrable spectral density.

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Authors and Affiliations

  1. Kiev Polytechnic Institute, Kiev

    V. V. Buldygin

  2. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    V. V. Zayats

Authors
  1. V. V. Buldygin
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  2. V. V. Zayats
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 11, pp. 1485–1497, November, 1995.

This work was financially supported by the Ukrainian State Committee on Science and Technology.

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Buldygin, V.V., Zayats, V.V. On asymptotic normality of estimates for correlation functions of stationary Gaussian processes in the space of continuous functions. Ukr Math J 47, 1696–1710 (1995). https://doi.org/10.1007/BF01057918

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  • DOI: https://doi.org/10.1007/BF01057918

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