Improved Portmanteau Diagnostic Test for Multivariate Time Series Using Monte-Carlo Techniques

• Activity Number: 534
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Esam Mahdi*+ and A. Ian McLeod
• Companies: The University of Western Ontario and The University of Western Ontario
• Keywords: Diagnostic check ; Monte-Carlo test ; Portmanteau test ; Multivariate time series ; VARMA models ; Parallel computing

Abstract

A new multivariate portmanteau test, based on Monte-Carlo technique is proposed. The proposed test is the determinant of the mth block matrix of cross autocorrelation matrices, where the Hosking's definition of the sample correlation matrix is used. This test can be considered as an extension to the multivariate case of the univariate test of Pena and Rodriguez. It is shown, depending on the model, the nominal size, and the sample size, that this test can be up to 3 times more powerful than the ones proposed by Hosking and Li and McLeod. It estimates the significance level accurately, with the highest power, and one can easily implement this test in quantitative programming environment such as Mathematica, R, and SAS. An illustrative application to var model diagnostic checking is given.