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Goodness-of-Fit Tests for Stationary Gaussian Processes with Tapered Data

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Abstract

The paper is concerned with the construction of goodness-of-fit tests for testing a hypothesis \(H_{0}\) that the hypothetical spectral density of a stationary Gaussian process \(X(t)\) has the specified form, based on the tapered data. We show that in the case where the hypothetical spectral density of \(X(t)\) does not depend on unknown parameters (the hypothesis \(H_{0}\) is simple), then the suggested test statistic has a limiting chi-square distribution. In the case where the hypothesis \(H_{0}\) is composite, that is, the hypothetical spectral density of \(X(t)\) depends on an unknown parameter, we choose an appropriate estimator for unknown parameter and describe the limiting distribution of the test statistic. This distribution is similar to that of obtained by Chernov and Lehman (Ann. Math. Stat. 25(3):579–586, 1954) in the case of independent observations.

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Acknowledgements

The author would like to thank the referees for their careful review of the manuscript and valuable comments and suggestions.

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  1. Department of Mathematics and Statistics, Boston University, 111 Cummington Mall, Boston, MA, 02215, USA

    Mamikon S. Ginovyan

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  1. Mamikon S. Ginovyan
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Correspondence to Mamikon S. Ginovyan.

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The research was partially supported by National Science Foundation Grant #DMS-1309009 at Boston University.

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Ginovyan, M.S. Goodness-of-Fit Tests for Stationary Gaussian Processes with Tapered Data. Acta Appl Math 171, 1 (2021). https://doi.org/10.1007/s10440-020-00368-0

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