Graphical Gaussian modelling of multivariate time series with latent variables

Michael Eichler; JMLR W&CP 9:193-200, 2010.

Abstract

In time series analysis, inference about cause-effect relationships among multiple times series is commonly based on the concept of Granger causality, which exploits temporal structure to achieve causal ordering of dependent variables. One major problem in the application of Granger causality for the identification of causal relationships is the possible presence of latent variables that affect the measured components and thus lead to so-called spurious causalities. In this paper, we describe a new graphical approach for modelling the dependence structure of multivariate stationary time series that are affected by latent variables. To this end, we introduce dynamic maximal ancestral graphs (dMAGs), in which each time series is represented by a single vertex. For Gaussian processes, this approach leads to vector autoregressive models with errors that are not independent but correlated according to the dashed edges in the graph. We discuss identifiability of the parameters and show that these models can be viewed as graphical ARMA models that satisfy the Granger causality restrictions encoded by the associated dynamic maximal ancestral graph.



Home Page

Papers

Submissions

News

Scope

Editorial Board

Announcements

Proceedings

Open Source Software

Search

Login



RSS Feed

Page last modified on Wed Mar 24 15:36 GMT 2010.

Copyright @ JMLR 2000. All rights reserved.