Causality in Time Series - ClopiNet

JMLR: Workshop and Conference Proceedings 12:1–29Linking Granger Causality and the Pearl Causal Model withSettable SystemsHalbert WhiteDepartment of EconomicsUniversity of California, San DiegoLa Jolla, CA 92093Karim ChalakDepartment of EconomicsBoston College140 Commonwealth AvenueChestnut Hill, MA 02467Xun LuDepartment of EconomicsHong Kong University of Science and TechnologyClear Water Bay, Hong Konghwhite@ucsd.educhalak@bc.eduxunlu@ust.hkEditors: Florin Popescu and Isabelle GuyonAbstractThe causal notions embodied in the concept of Granger causality have been arguedto belong to a different category than those of Judea Pearl’s Causal Model, and sofar their relation has remained obscure. Here, we demonstrate that these conceptsare in fact closely linked by showing how each relates to straightforward notions ofdirect causality embodied in settable systems, an extension and refinement of the PearlCausal Model designed to accommodate optimization, equilibrium, and learning. Wethen provide straightforward practical methods to test for direct causality using testsfor Granger causality.Keywords: Causal Models, Conditional Exogeneity, Conditional Independence, GrangerNon-causality1. IntroductionThe causal notions embodied in the concept of Granger causality (“G−causality") (e.g.,Granger, C.W.J., 1969; Granger, C.W.J. and P. Newbold, 1986) are probabilistic, relatingto the ability of one time series to predict another, conditional on a given informationset. On the other hand, the causal notions of the Pearl Causal Model (“PCM")(e.g., Pearl, J., 2000) involve specific notions of interventions and of functional ratherthan probabilistic dependence. The relation between these causal concepts has so farremained obscure. For his part, Granger, C.W.J. (1969) acknowledged that G−causalitywas not “true" causality, whatever that might be, but that it seemed likely to be an importantpart of the full story. On the other hand, Pearl, J. (2000, p. 39) states thatc○ H. White, K. Chalak & X. Lu.