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

Michael W. Robbins and Thomas J. Fisher

Journal of Business & Economic Statistics, 2015, vol. 33, issue 4, 459-473

Abstract: An often-studied problem in time series analysis is that of testing for the independence of two (potentially multivariate) time series. Toeplitz matrices have demonstrated utility for the related setting of time series goodness-of-fit testing--ergo, herein, we extend those concepts by defining a nontrivial block Toeplitz matrix for use in the setting of independence testing. We propose test statistics based on the trace of the square of the matrix and determinant of the matrix; these statistics are connected to one another as well as known statistics previously proposed in the literature. 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 that are asymptotically equivalent under the null hypothesis. Additionally, 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, which include the famous Granger causality test. Finally, data examples involving U.S. inflation, trade volume, and exchange rates are given. Supplementary materials for this article are available online.

Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://hdl.handle.net/10.1080/07350015.2014.962699 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlbes:v:33:y:2015:i:4:p:459-473

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/UBES20

DOI: 10.1080/07350015.2014.962699

Access Statistics for this article

Journal of Business & Economic Statistics is currently edited by Eric Sampson, Rong Chen and Shakeeb Khan

More articles in Journal of Business & Economic Statistics from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().