Optimal tests of noncorrelation between multivariate time series

• 成果类型: Article
• 署名作者: Hallin, Marc; Saidi, Abdessamad
• 署名单位: Universite Libre de Bruxelles; Universite de Montreal
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214507000000239
• 发表日期: 2007
• 页码: 938-951
• 关键词: Adaptive Estimation; INDEPENDENCE; causality

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.