A Generalized Portmanteau Test for Independence of Two Infinite Order Vector Autoregressive Series

• Activity Number: 55
• Type: Contributed
• Date/Time: Sunday, August 3, 2003 : 4:00 PM to 5:50 PM
• Sponsor: Business & Economics Statistics Section
• Author(s): Bouhaddioui Chafik*+ and Roch Roy
• Companies: University of Montreal and University of Montreal
• Keywords: infinite order vector autoregressive process ; independence ; residual cross-correlation ; kernel function ; portmanteau statistic ; asymptotic power

Abstract

In many situations, we want to verify the existence of a relationship between multivariate time series. Here, we propose a semiparametric approach for testing the independence between two infinite order vector autoregressive series which is an extension of Hong's (1996) univariate results. We first filter each series by a finite autoregression, and the test statistic is a standardized version of the sum of weighted squared residual cross-correlation at all possible lags. The weights depend on a kernel function and on a truncation parameter. Using a result of Lewis and Reinsel (1985), the asymptotic distribution of the statistic test is derived under the null hypothesis and its consistency is also established for a fixed alternative of unknown form. Apart of standardization factors, the multivariate portmanteau statistic proposed by Bouhaddioui and Roy (2002) that takes into account a fixed number of lags can be viewed as a special case by using the truncated uniform kernel. However, many kernels lead to a greater power, as shown in a local and global asymptotic power analysis and by a small simulation study in finite samples. A numerical example with real data is also presented.