Detecting Co-Movements in Non-Causal Time Series

Gianluca Cubadda, Alain Hecq*, Sean Telg

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

This paper introduces the notion of common non-causal features and proposes tools to detect them in multivariate time series models. We argue that the existence of co-movements might not be detected using the conventional stationary vector autoregressive (VAR) model as the common dynamics are present in the non-causal (i.e. forward-looking) component of the series. We show that the presence of a reduced rank structure allows to identify purely causal and non-causal VAR processes of order P>1 even in the Gaussian likelihood framework. Hence, usual test statistics and canonical correlation analysis can be applied, where either lags or leads are used as instruments to determine whether the common features are present in either the backward- or forward-looking dynamics of the series. The proposed definitions of co-movements are also valid for the mixed causal—non-causal VAR, with the exception that a non-Gaussian maximum likelihood estimator is necessary. This means however that one loses the benefits of the simple tools proposed. An empirical analysis on Brent and West Texas Intermediate oil prices illustrates the findings. No short run co-movements are found in a conventional causal VAR, but they are detected when considering a purely non-causal VAR.

Original languageEnglish
Pages (from-to)697-715
Number of pages19
JournalOxford Bulletin of Economics and Statistics
Volume81
Issue number3
DOIs
Publication statusPublished - 1 Jun 2019
Externally publishedYes

Funding

JEL Classification numbers: C12, C32, E32. *Previous versions of this paper have been presented at conferences of the Society for Nonlinear Dynamics and Econometrics (Oslo, March 2015), the International Association for Applied Econometrics-IAAE (Tessaloniki, June 2015), the Netherlands Econometric Study Group (Maastricht, May 2015), the International Symposium on Forecasting (Santander, June 2016), the Computational and Financial Econometrics (Sevilla, December 2016), the Brazilian Econometric Society (Iguassu, December 2016), the Scientific Meeting of the Italian Statistical Society (Palermo, June 2018) as well as at seminars at the University of Balear Islands (Palma, November 2015), SKKU (Seoul, January 2016), Aix-Marseille (Marseille, March 2016), KU Leuven (Leuven, March 2016), FGV (Rio de Janeiro, May 2016). We thank the participants for helpful comments and suggestions. Additionally, we are greatly in debt to Lenard Lieb for fruitful discussions and two anonymous referees for valuable comments and suggestions.

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