Optimal tests of noncorrelation between multivariate time series

被引:4
作者
Hallin, Marc [1 ]
Saidi, Abdessamad
机构
[1] ECARES, Inst Res Stat, Brussels, Belgium
[2] Univ Libre Bruxelles, Dept Math, Brussels, Belgium
[3] Univ Montreal, Dept Res Math & Stat, Montreal, PQ H3C 3J7, Canada
关键词
Haugh-El Himdi-Roy tests; Koch-Yang-Hallin-Saidi tests; local asymptotic normality; tests of noncorrelation; time series; vector autoregressive model;
D O I
10.1198/016214507000000239
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
The problem of testing noncorrelation between two multivariate time series is considered. Assuming that the global process admits a joint vector autoregressive (VAR) representation, noncorrelation between the two component series is equivalent to the hypothesis that all off-diagonal blocks in the matrix coefficients and the innovation covariance of the joint VAR representation are zero. We establish an adequate local asymptotic normality (LAN) property for this VAR model in the vicinity of noncorrelation. This LAN structure allows construction of optimal pseudo-Gaussian tests-that is, tests that are locally and asymptotically optimal under Gaussian innovations, but remain valid under non-Gaussian ones-for the null hypothesis of noncorrelation and for comparing their local asymptotic powers with those of the heuristic tests (Haugh-El Himdi-Roy and Koch-Yang-Hallin-Saidi) proposed in the literature.
引用
收藏
页码:938 / 951
页数:14
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