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Extracting informative variables in the validation of two-group causal relationship

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Abstract

The validation of causal relationship between two groups of multivariate time series data often requires the precedence knowledge of all variables. However, in practice one finds that some variables may be negligible in describing the underlying causal structure. In this article we provide an explicit definition of “non-informative variables” in a two-group causal relationship and introduce various automatic computer-search algorithms that can be utilized to extract informative variables based on a hypothesis testing procedure. The result allows us to represent a simplified causal relationship by using minimum possible information on two groups of variables.

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References

  • Arnold A, Liu Y, Abe N (2007) Temporal causal modeling with graphical Granger methods. In: Proceedings of the 13th ACM SIGKDD international conference on knowledge discovery and data mining, pp 66–75

  • Boudjellaba H, Dufour JN, Roy R (1992) Testing causality between two vectors in multivariate autoregressive moving average models. J Am Stat Assoc 87:1082–1090

    Article  MathSciNet  MATH  Google Scholar 

  • Dufour JM, Renault E (1998) Short-run and long-run causality in time series theory. Econometrica 66: 1099–1125

    Article  MathSciNet  MATH  Google Scholar 

  • Fujita A, Sato JR, Garay-Malpartida HM, Morettin PA, Sogayar MC, Ferreira CE (2007) Time-varying modeling of gene expression regulatory networks using the wavelet dynamic vector autoregressive method. Bioinformatics 23:1623–1630

    Article  Google Scholar 

  • Geweke J (1982) Measurement of linear dependence and feedback between multiple time series. J Am Stat Assoc 77:304–313

    Article  MathSciNet  MATH  Google Scholar 

  • Geweke J (1984) Inference and causality in economic time series. In: Griliches Z, Intriligator MM (eds) Handbook of econometrics, vol 2. North-Holland, Amsterdam, pp 1101–1144

    Chapter  Google Scholar 

  • Granger CWJ (1969) Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37:424–438

    Article  Google Scholar 

  • Granger CWJ (1980) Testing for causality: a personal viewpoint. J Econ Dyn Control 2:329–352

    Article  MathSciNet  Google Scholar 

  • Granger CWJ, Lin JL (1995) Causality in the long run. Econ Theory 11:530–536

    Article  Google Scholar 

  • Hacker RS, Hatemi JA (2006) Tests for causality between integrated variables using asymptotic and bootstrap distributions: theory and application. Appl Econ 38:1489–1500

    Article  Google Scholar 

  • Haufe S, Müller K-R, Nolte G, Krämer N (2010) Sparse causal discovery in multivariate time series. In: NIPS 2008 workshop on causality. JMLR workshop and conference proceedings, vol 6, pp 97–106

  • Hsiao C (1982) Autoregressive modeling and causal ordering of econometric variables. J Econ Dyn Control 4:243–259

    Article  Google Scholar 

  • Koster JTA (1996) Markov properties of nonrecursive causal models. Ann Stat 24:2148–2177

    Article  MathSciNet  MATH  Google Scholar 

  • Koster JTA (1999) On the validity of the Markov interpretation of path diagrams of Gaussian structural equations systems with correlated errors. Scand J Stat 26:413–431

    Article  MathSciNet  MATH  Google Scholar 

  • Kutner MH, Nachtsheim CJ, Neter J (2008) Applied linear regression models, 4th edn. McGraw Hill, New York

    Google Scholar 

  • Lauritzen SL (1996) Graphical models. Oxford University Press, Oxford

    Google Scholar 

  • Lauritzen SL (2000) Causal inference from graphical models. In: Barndorff-Nielsen E, Cox DR, Klüppelberg C (eds) Complex stochastic systems. CRC Press, London

    Google Scholar 

  • Lütkepohl H (2005) New introduction to multiple time series analysis, 1st edn. 2nd printing, Springer, Berlin

  • Lütkepohl H, Burda MM (1997) Modified Wald tests under nonregular conditions. J Econ 78:315–332

    MATH  Google Scholar 

  • Makridakis SG, Wheelwright SC, McGee VE (1983) Forecasting: methods and applications. Wiley, New York

    Google Scholar 

  • Mosconi R, Giannine C (1992) Non-causality in cointegrated system: representation. Estimation and testing. Oxf Bull Econ Stat 54:399–417

    Article  Google Scholar 

  • Osborn DR (1984) Causality testing and its implication for dynamic econometric models. Econ J 94:82–96

    Article  Google Scholar 

  • Pearl J (1995) Causal diagrams for empirical research (with discussion). Biometrika 82:669–710

    Article  MathSciNet  MATH  Google Scholar 

  • Pearl J (2000) Causality: models, reasoning, and inference. Cambridge University Press, Cambridge

    Google Scholar 

  • Roebroech A, Formisano E, Goebel R (2005) Mapping directed influence over the brain using Granger causality and fMRI. NeuroImage 25:230–242

    Article  Google Scholar 

  • Whittaker J (1990) Graphical models in applied multivariate statistics. Wiley, Chichester

    MATH  Google Scholar 

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Correspondence to Neng-Fang Tseng.

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Hung, YC., Tseng, NF. Extracting informative variables in the validation of two-group causal relationship. Comput Stat 28, 1151–1167 (2013). https://doi.org/10.1007/s00180-012-0351-z

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  • DOI: https://doi.org/10.1007/s00180-012-0351-z

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