Cross-Correlation Matrices for Tests of Independence and Causality Between Two Multivariate Time Series

• Activity Number: 32
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Michael Robbins*+
• Companies: RAND Corporation
• Keywords: Causality ; Independence ; Multivariate Time Series ; Granger Causality ; Vector ARMA

Abstract

An often studied problem in time series analysis is that of testing for the independence of two (multivariate) time series. Toeplitz matrices have demonstrated utility for the related setting of time series goodness-of-fit testing; those concepts are extended by defining a nontrivial block Toeplitz matrix for use in the setting of independence testing. Test statistics based on the trace of the square of the matrix and determinant of the matrix are proposed; these statistics are connected to one another as well as known statistics. Furthermore, the log of the determinant is argued to relate to a likelihood ratio test and is proven to be more powerful than other tests which are asymptotically equivalent under the null hypothesis. Also, matrix-based tests are presented for the purpose of inferring the location or direction of the causality existing between the two series. A simulation study is provided to explore the efficacy of the proposed methodology; the methods are shown to offer improvement over existing techniques, including the famous Granger causality test. Data examples involving US inflation, trade volume and exchange rates are given.