Graphical Gaussian modelling of multivariate time series with latent variables

Michael Eichler
Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, PMLR 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v9-eichler10a, title = {Graphical Gaussian modelling of multivariate time series with latent variables}, author = {Eichler, Michael}, booktitle = {Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics}, pages = {193--200}, year = {2010}, editor = {Teh, Yee Whye and Titterington, Mike}, volume = {9}, series = {Proceedings of Machine Learning Research}, address = {Chia Laguna Resort, Sardinia, Italy}, month = {13--15 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v9/eichler10a/eichler10a.pdf}, url = {https://proceedings.mlr.press/v9/eichler10a.html}, 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.} }
Endnote
%0 Conference Paper %T Graphical Gaussian modelling of multivariate time series with latent variables %A Michael Eichler %B Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2010 %E Yee Whye Teh %E Mike Titterington %F pmlr-v9-eichler10a %I PMLR %P 193--200 %U https://proceedings.mlr.press/v9/eichler10a.html %V 9 %X 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.
RIS
TY - CPAPER TI - Graphical Gaussian modelling of multivariate time series with latent variables AU - Michael Eichler BT - Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics DA - 2010/03/31 ED - Yee Whye Teh ED - Mike Titterington ID - pmlr-v9-eichler10a PB - PMLR DP - Proceedings of Machine Learning Research VL - 9 SP - 193 EP - 200 L1 - http://proceedings.mlr.press/v9/eichler10a/eichler10a.pdf UR - https://proceedings.mlr.press/v9/eichler10a.html AB - 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. ER -
APA
Eichler, M.. (2010). Graphical Gaussian modelling of multivariate time series with latent variables. Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 9:193-200 Available from https://proceedings.mlr.press/v9/eichler10a.html.

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