## Abstract

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 hy-potheses 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.

Original language | English |
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Pages (from-to) | 3529-3554 |

Number of pages | 26 |

Journal | Annals of Statistics |

Volume | 37 |

Issue number | 6 A |

DOIs | |

Publication status | Published - 2009 Dec |

## Keywords

- Multivariate time series
- Nonparametric testing
- Semiparametric testing
- Spectral analysis

## ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty