Detecting Co-Movements in Noncausal Time Series

37 Pages Posted: 3 May 2018

See all articles by Gianluca Cubadda

Gianluca Cubadda

University of Rome Tor Vergata - Department of Economics and Finance

Alain Hecq

Maastricht University - Department of Quantitative Economics

Sean Telg

Maastricht University - Department of Quantitative Economics

Date Written: April 20, 2018

Abstract

This paper introduces the notion of common noncausal 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 noncausal (i.e. forward-looking) component of the series. In particular, we show that the presence of a reduced rank structure allows to identify purely causal and noncausal VAR processes of order two and higher even in the Gaussian likelihood framework. Hence, usual test statistics and canonical correlation analysis can still be applied, where both lags and 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 de finitions of co-movements also valid for the mixed causal-noncausal VAR, with the exception that an approximate non-Gaussian maximum likelihood estimator is necessary for these cases. This means however that one loses the bene fits of the simple tools proposed in this paper. An empirical analysis on European Brent and U.S. West Texas Intermediate oil prices illustrates the main fi ndings. Whereas we fail to fi nd any short run co-movements in a conventional causal VAR, they are detected in the growth rates of the series when considering a purely noncausal VAR.

Keywords: causal and noncausal process, common features, vector autoregressive models, oil prices

JEL Classification: C12, C32, E32.

Suggested Citation

Cubadda, Gianluca and Hecq, Alain and Telg, Sean, Detecting Co-Movements in Noncausal Time Series (April 20, 2018). CEIS Working Paper No. 430. Available at SSRN: https://ssrn.com/abstract=3166097 or http://dx.doi.org/10.2139/ssrn.3166097

Gianluca Cubadda

University of Rome Tor Vergata - Department of Economics and Finance ( email )

Via Columbia n.2
Roma, 00133
Italy

Alain Hecq (Contact Author)

Maastricht University - Department of Quantitative Economics ( email )

P.O. Box 616
Maastricht, 6200 MD
Netherlands

HOME PAGE: http://www.maastrichtuniversity.nl/a.hecq

Sean Telg

Maastricht University - Department of Quantitative Economics ( email )

P.O. Box 616
Maastricht, 6200 MD
Netherlands

HOME PAGE: http://www.maastrichtuniversity.nl/j.telg

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