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Search for additive nonlinear time series causal models
 JMLR
, 2008
"... Pointwise consistent, feasible procedures for estimating contemporaneous linear causal structure from time series data have been developed using multiple conditional independence tests, but no such procedures are available for nonlinear systems. We describe a feasible procedure for learning a class ..."
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Pointwise consistent, feasible procedures for estimating contemporaneous linear causal structure from time series data have been developed using multiple conditional independence tests, but no such procedures are available for nonlinear systems. We describe a feasible procedure for learning a class of nonlinear time series structures, which we call additive nonlinear time series. We show that for data generated from stationary models of this type, two classes of conditional independence relations among time series variables and their lags can be tested efficiently and consistently using tests based on additive model regression. Combining results of statistical tests for these two classes of conditional independence relations and the temporal structure of time series data, a new consistent model specification procedure is able to extract relatively detailed causal information. We investigate the finite sample behavior of the procedure through simulation, and illustrate the application of this method through analysis of the possible causal connections among four ocean indices. Several variants of the procedure are also discussed.
Graphical modelling of multivariate time series with latent variables
, 2005
"... Abstract. In time series analysis, inference about causee®ect 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 causali ..."
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Abstract. In time series analysis, inference about causee®ect 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 identi¯cation of causal relationships is the possible presence of latent variables that a®ect the measured components and thus lead to socalled spurious causalities. In this paper, we describe a new graphical approach for modelling the dependence structure of multivariate stationary time series that are a®ected by latent variables. Is is based on mixed graphs in which directed edges represent direct in°uences among the variables while dashed edgesdirected or undirectedindicate associations that are induced by latent variables. For Gaussian processes, this approach leads to vector autoregressive processes with errors that are not independent but correlated according to the dashed edges in the graph. We show that these models can be viewed as graphical ARMA models that satisfy the Granger causality restrictions encoded by general mixed graphs. We discuss identi¯ability of the parameters and illustrate the approach by an example. 1.
Changing sets of parameters by partial mappings
"... Abstract: Changes between different sets of parameters are needed in multivariate statistical modeling. There may, for instance, be specific inference questions based on subject matter interpretations, alternative wellfitting constrained models, compatibility judgements of seemingly distinct constr ..."
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Abstract: Changes between different sets of parameters are needed in multivariate statistical modeling. There may, for instance, be specific inference questions based on subject matter interpretations, alternative wellfitting constrained models, compatibility judgements of seemingly distinct constrained models, and different reference priors under alternative parameterizations. We introduce and discuss a partial mapping, called partial replication, and derive from it a more complex mapping, called partial inversion. Both operations are shown to be tools for decomposing matrix operations, for explaining recursion relations among sets of linear parameters, for deriving effects of omitted variables in alternative model formulations, for changing between different types of linear chain graph models, for approximating maximumlikelihood estimates in exponential family models under independence constraints, and for switching partially between sets of canonical and moment parameters in distributions of the exponential family or between sets of corresponding maximumlikelihood estimates. Key words and phrases: Exponential family, graphical Markov models, independence