Mathematics – Statistics Theory
Scientific paper
2009-09-02
Annals of Statistics 2009, Vol. 37, No. 6A, 3529-3554
Mathematics
Statistics Theory
Published in at http://dx.doi.org/10.1214/08-AOS610 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Scientific paper
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.
Matsuda Yasumasa
Yajima Yoshihiro
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