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Testing for independence between two covariance stationary time series. (English) Zbl 1029.62500
A one-sided asymptotically normal test for independence between two stationary time series is proposed by first prewhitening the two time series and then basing the test on the residual cross-correlation function. The test statistic is a properly standardised version of the sum of weighted squares of residual cross-correlations, with weights depending on a kernel function. L.D. Haugh’s [J. Am. Stat. Assoc. 71, 378-385 (1976; Zbl 0337.62061)] test can be viewed as a special case of our approach in the sense that it corresponds to the use of the truncated kernel. Many kernels deliver better power than Haugh’s test. A simulation study shows that the new test has good power against short and long cross-correlations.

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F05 Asymptotic properties of parametric tests
62G10 Nonparametric hypothesis testing
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