A Nonparametric Causality Test: Detection of Direct Causal Effects in Multivariate Systems Using Corrected Partial Transfer Entropy

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In a recent work we proposed the corrected transfer entropy (CTE), which reduces the bias in the estimation of transfer entropy (TE), a measure of Granger causality for bivariate time series making use of the conditional mutual information. An extension of TE to account for the presence of other time series is the partial TE (PTE). Here, we propose the correction of PTE, termed Corrected PTE (CPTE), in a similar way to CTE: time shifted surrogates are used in order to quantify and correct the bias, and the estimation of the involved entropies of high-dimensional variables is made with the method of k-nearest neighbors. CPTE is evaluated on coupled stochastic systems with both linear and nonlinear interactions. Finally, we apply CPTE to economic data and investigate whether we can detect the direct causal effects among economic variables.