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Conditional independence graph for nonlinear time series and its application to international financial markets Wei Gao a,∗ , Hongxia Zhao b
School of Statistics, Xi’an University of Finance and Economics, Xi’an Shaanxi 710061, China School of College English, Xi’an University of Finance and Economics, Xi’an Shaanxi 710061, China
Conditional independence graphs are proposed for describing the dependence structure of multivariate nonlinear time series, which extend the graphical modeling approach based on partial correlation. The vertexes represent the components of a multivariate time series and edges denote direct dependence between corresponding series. The conditional independence relations between component series are tested efficiently and consistently using conditional mutual information statistics and a bootstrap procedure. Furthermore, a method combining information theory with surrogate data is applied to test the linearity of the conditional dependence. The efficiency of the methods is approved through simulation time series with different linear and nonlinear dependence relations. Finally, we show how the method can be applied to international financial markets to investigate the nonlinear independence structure. © 2012 Elsevier B.V. All rights reserved.
Article history: Available online 14 March 2013 Keywords: Nonlinear time series Conditional independence graphs Conditional mutual information Financial markets
1. Introduction In recent years increasing research studies involved the interaction structure between national stock markets and many empirical works in financial data used graphical models, e.g. Refs. [1,2]. Allali et al.  applied a partial correlation graph to study the interaction structure between international markets and investigated the...