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.

本文关注于拟合假设检验（H_ {0} \）的拟合优度检验的构造，该假设是固定高斯过程\（X（t）\）的假设光谱密度具有指定形式，基于在锥形数据上。我们表明，在假设\（X（t）\）的光谱密度不依赖于未知参数的情况下（假设\（H_ {0} \）很简单），则建议的检验统计量具有局限性平方分布。在假设\（H_ {0} \）是合成的情况下，即\（X（t）\）的假设光谱密度取决于未知参数，我们为未知参数选择合适的估计量，并描述检验统计量的极限分布。在独立观察的情况下，这种分布类似于Chernov和Lehman所获得的分布（Ann。Math。Stat。25（3）：579-586，1954）。