Open Access
December 2009 On nonparametric and semiparametric testing for multivariate linear time series
Yoshihiro Yajima, Yasumasa Matsuda
Ann. Statist. 37(6A): 3529-3554 (December 2009). DOI: 10.1214/08-AOS610


We formulate nonparametric and semiparametric hypothesis testing of multivariate stationary linear time series in a unified fashion and propose new test statistics based on estimators of the spectral density matrix. The limiting distributions of these test statistics under null hypotheses are always normal distributions, and they can be implemented easily for practical use. If null hypotheses are false, as the sample size goes to infinity, they diverge to infinity and consequently are consistent tests for any alternative. The approach can be applied to various null hypotheses such as the independence between the component series, the equality of the autocovariance functions or the autocorrelation functions of the component series, the separability of the covariance matrix function and the time reversibility. Furthermore, a null hypothesis with a nonlinear constraint like the conditional independence between the two series can be tested in the same way.


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Yoshihiro Yajima. Yasumasa Matsuda. "On nonparametric and semiparametric testing for multivariate linear time series." Ann. Statist. 37 (6A) 3529 - 3554, December 2009.


Published: December 2009
First available in Project Euclid: 17 August 2009

zbMATH: 1369.62246
MathSciNet: MR2549568
Digital Object Identifier: 10.1214/08-AOS610

Primary: 62M15
Secondary: 62M07 , 62M10

Keywords: multivariate time series , Nonparametric testing , semiparametric testing , spectral analysis

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 6A • December 2009
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