The comparison of two time series often arises in climatology, environmental science, and econometrics. Through natural and physical circumstances these series are often dependent. We develop a hypothesis test for the equality of autocovariance functions for two linearly dependent multivariate time series. Previous tests for two independent series are reviewed and extended to the dependent case. A univariate bootstrapped statistic that automatically selects the order of the test is extended to the multivariate setting as well. The performance of the tests are compared through simulation and the methods are applied to univariate temperature and multivariate air quality series. Empirical results show that by accounting for the correlation between series substantial improvements in power can be made in the detection of differences in the autocovariance.

中文翻译：

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关于测试时间序列中自协方差的相等性

两个时间序列的比较经常出现在气候学、环境科学和计量经济学中。通过自然和物理环境，这些系列通常是相互依赖的。我们为两个线性相关的多元时间序列的自协方差函数的相等性开发了一个假设检验。回顾了先前对两个独立系列的测试并将其扩展到相关案例。自动选择测试顺序的单变量自举统计也扩展到多变量设置。通过模拟比较了测试的性能，并将方法应用于单变量温度和多变量空气质量系列。