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首页> 外文期刊>Journal of Time Series Analysis >Tests for the Equality of Two Processes' Spectral Densities with Unequal Lengths Using Wavelet Methods
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Tests for the Equality of Two Processes' Spectral Densities with Unequal Lengths Using Wavelet Methods

机译：用小波方法检验长度不相等的两个过程的光谱密度是否相等

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摘要

Testing procedures for assessing whether two stationary and independent linear processes with unequal lengths have the same spectral densities or same auto-covariance functions are investigated. New test statistics are proposed based on the difference of the two wavelet-based estimates of the two spectral densities. The asymptotic normal distributions of the empirical wavelet coefficients are derived based on Bartlett type approximation of a quadratic form with dependent variables by the corresponding quadratic form with independent and identically distributed (i.i.d.) random variables. The limit distributions of the proposed test statistics are derived from those asymptotic results, and they asymptotically follow known chi-square distributions. The advantage of those new procedures is that those test statistics are constructed very simply and can be used for two time series with arbitrary lengths. The performance of those new tests is compared with some recent test statistics, with respect to their exact levels and powers. Simulation studies show that our proposed tests are very comparable to the current tests.
机译：研究了用于评估长度不相等的两个固定且独立的线性过程是否具有相同的光谱密度或相同的自协方差函数的测试程序。基于两个基于小波的两个光谱密度估计值的差异，提出了新的测试统计数据。经验小波系数的渐近正态分布是基于具有因变量的二次形式的Bartlett类型逼近，通过具有独立且均布的（i.d.d）随机变量的对应二次形式来得出的。拟议的测试统计量的极限分布是从这些渐近结果中得出的，它们渐近遵循已知的卡方分布。这些新过程的优点在于，这些测试统计信息的构建非常简单，并且可以用于任意长度的两个时间序列。将这些新测试的性能与最近的一些测试统计数据进行比较，以了解它们的确切级别和功效。仿真研究表明，我们提出的测试与当前测试非常可比。

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