Trimmed Granger causality between two groups of time series

Abstract: The identification of causal effects between two groups of time series has been an important topic in a wide range of applications such as economics, engineering, medicine, neuroscience, and biology. In this paper, a simplified causal relationship (called trimmed Granger causality) based on the context of Granger causality and vector autoregressive (VAR) model is introduced. The idea is to characterize a subset of “important variables” for both groups of time series so that the underlying causal structure can be presented based on minimum variable information. When the VAR model is specified, explicit solutions are provided for the identification of important variables. When the parameters of the VAR model are unknown, an efficient statistical hypothesis testing procedure is introduced to estimate the solution. An example representing the stock indices of different countries is used to illustrate the proposed methods. In addition, a simulation study shows that the proposed methods significantly outperform the Lasso-type methods in terms of the accuracy of characterizing the simplified causal relationship.

[1]  Sterling K. Berberian,et al.  Introduction to Hilbert Space , 1977 .

[2]  Rupert G. Miller.  Simultaneous Statistical Inference , 1966 .

[3]  Z. Šidák.  ON MULTIVARIATE NORMAL PROBABILITIES OF RECTANGLES: THEIR DEPENDENCE ON CORRELATIONS' , 1968 .

[4]  D. Luenberger.  Optimization by Vector Space Methods , 1968 .

[5]  Z. Šidák.  On Probabilities of Rectangles in Multivariate Student Distributions: Their Dependence on Correlations , 1971 .

[6]  R. R. Hocking.  The analysis and selection of variables in linear regression , 1976 .

[7]  S. Holm.  A Simple Sequentially Rejective Multiple Test Procedure , 1979 .

[8]  C. Sims.  MACROECONOMICS AND REALITY , 1977 .

[9]  K. Worsley.  An improved Bonferroni inequality and applications , 1982 .

[10]  J. Geweke,et al.  Measurement of Linear Dependence and Feedback between Multiple Time Series , 1982 .

[11]  John Geweke,et al.  Inference and causality in economic time series models , 1984 .

[12]  R. Simes,et al.  An improved Bonferroni procedure for multiple tests of significance , 1986 .

[13]  Y. Hochberg.  A sharper Bonferroni procedure for multiple tests of significance , 1988 .

[14]  Alan J. Miller.  Subset Selection in Regression , 1992 .

[15]  R. Mosconi,et al.  NON-CAUSALITY IN COINTEGRATED SYSTEMS: REPRESENTATION ESTIMATION AND TESTING , 1992 .

[16]  Jean-Marie Dufour,et al.  Testing Causality between Two Vectors in Multivariate Autoregressive Moving Average Models , 1992 .

[17]  Helmut Lütkepohl,et al.  Testing for Causation Between Two Variables in Higher-Dimensional VAR Models , 1993 .

[18]  Jean-Marie Dufour,et al.  Short-Run and Long-Rub Causality in Time Series: Theory. , 1998 .

[19]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[20]  Helmut Lütkepohl,et al.  Modified wald tests under nonregular conditions , 1997 .

[21]  CopelandMaggie,et al.  Leads, Lags, and Trading in Global Markets , 1998 .

[22]  Jin-Gil Jeong.  Cross-border transmission of stock price volatility: evidence from the overlapping trading hours , 1999 .

[23]  C. Granger.  Investigating causal relations by econometric models and cross-spectral methods , 1969 .

[24]  Rainer Goebel,et al.  Mapping directed influence over the brain using Granger causality and fMRI , 2005, NeuroImage.

[25]  Abdulnasser Hatemi-J,et al.  Tests for causality between integrated variables using asymptotic and bootstrap distributions: theory and application , 2006 .

[26]  João Ricardo Sato,et al.  Time-varying modeling of gene expression regulatory networks using the wavelet dynamic vector autoregressive method , 2007, Bioinform..

[27]  Yan Liu,et al.  Temporal causal modeling with graphical granger methods , 2007, KDD '07.

[28]  Helmut Ltkepohl,et al.  New Introduction to Multiple Time Series Analysis , 2007 .

[29]  A. Aue,et al.  Break detection in the covariance structure of multivariate time series models , 2009, 0911.3796.

[30]  Ali Shojaie,et al.  Discovering graphical Granger causality using the truncating lasso penalty , 2010, Bioinform..

[31]  P. Bickel,et al.  Large Vector Auto Regressions , 2011, 1106.3915.

[32]  Guofu Zhou,et al.  International Stock Return Predictability: What is the Role of the United States? , 2010 .

[33]  Richard A. Davis,et al.  Sparse Vector Autoregressive Modeling , 2012, 1207.0520.

[34]  G. Michailidis,et al.  Estimation in High-dimensional Vector Autoregressive Models , 2013 .