Paper #1356

Title:

Geometric and long run aspects of Granger causality

Author:

Majid M. Al-Sadoon

Date:

January 2013

Abstract:

This paper extends multivariate Granger causality to take into account the subspaces along which Granger causality occurs as well as long run Granger causality. The properties of these new notions of Granger causality, along with the requisite restrictions, are derived and extensively studied for a wide variety of time series processes including linear invertible process and VARMA. Using the proposed extensions, the paper demonstrates that: (i) mean reversion in L2 is an instance of long run Granger non-causality, (ii) cointegration is a special case of long run Granger non-causality along a subspace, (iii) controllability is a special case of Granger causality, and finally (iv) linear rational expectations entail (possibly testable) Granger causality restriction along subspaces.

Keywords:

Granger causality, long run Granger causality, L2 -mean-reversion, p-mixing, cointegration, VARMA, controllability, Kalman Decomposition, linear rational expectations

JEL codes:

C10, C32, C51.

Area of Research:

Statistics, Econometrics and Quantitative Methods

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