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Discussion Paper

No. 2007-15 | April 10, 2007
Learning Causal Relations in Multivariate Time Series Data


Applying a probabilistic causal approach, we define a class of time series causal models (TSCM) based on stationary Bayesian networks. A TSCM can be seen as a structural VAR identified by the causal relations among the variables. We classify TSCMs into observationally equivalent classes by providing a necessary and sufficient condition for the observational equivalence. Applying an automated learning algorithm, we are able to consistently identify the data-generating causal structure up to the class of observational equivalence. In this way we can characterize the empirical testable causal orders among variables based on their observed time series data. It is shown that while an unconstrained VAR model does not imply any causal orders in the variables, a TSCM that contains some empirically testable causal orders implies a restricted SVAR model. We also discuss the relation between the probabilistic causal concept presented in TSCMs and the concept of Granger causality. It is demonstrated in an application example that this methodology can be used to construct structural equations with causal interpretations.

JEL Classification


Cite As

Pu Chen and Hsiao Chihying (2007). Learning Causal Relations in Multivariate Time Series Data. Economics Discussion Papers, No 2007-15, Kiel Institute for the World Economy.


Comments and Questions

anonymous - Referee Report
May 30, 2007 - 11:47

see attached file

anonymous - Referee Report
June 01, 2007 - 14:23

see attached file

anonymous - Referee Report
July 02, 2007 - 09:54

see attached file

Pu Chen, Hsiao Chihying - Response to Referee Reports
August 13, 2007 - 10:13

see attached file