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This chapter focuses on constructing goodness-of-fit tests for testing the hypothesis that the spectral density of a stationary Gaussian process has a specified form, using tapered data. We show that when the spectral density does not depend on unknown parameters-indicating a simple null hypothesis-the proposed test statistic follows a limiting chi-square distribution. In contrast, when the null hypothesis is composite, meaning that the spectral density depends on an unknown parameter, we select an appropriate estimator for this parameter and describe the limiting distribution of the test statistic. This testing procedure applies to both short- and long-memory models.

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Goodness-of-Fit Tests Based on the Tapered Data

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  • 发表日期：

    2025年

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  • Mamikon S. Ginovyan

摘要

This chapter focuses on constructing goodness-of-fit tests for testing the hypothesis that the spectral density of a stationary Gaussian process has a specified form, using tapered data. We show that when the spectral density does not depend on unknown parameters-indicating a simple null hypothesis-the proposed test statistic follows a limiting chi-square distribution. In contrast, when the null hypothesis is composite, meaning that the spectral density depends on an unknown parameter, we select an appropriate estimator for this parameter and describe the limiting distribution of the test statistic. This testing procedure applies to both short- and long-memory models.