Detecting Co‐Movements in Non‐Causal Time Series

19 Pages Posted: 16 Apr 2019

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: June 2019

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.

Suggested Citation

Cubadda, Gianluca and Hecq, Alain and Telg, Sean, Detecting Co‐Movements in Non‐Causal Time Series (June 2019). Oxford Bulletin of Economics and Statistics, Vol. 81, Issue 3, pp. 697-715, 2019. Available at SSRN: https://ssrn.com/abstract=3372510 or http://dx.doi.org/10.1111/obes.12281

Gianluca Cubadda (Contact Author)

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

Via Columbia n.2
Roma, 00133
Italy

Alain Hecq

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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