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Cause-Effect Pairs in Time Series with a Focus on Econometrics

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Cause Effect Pairs in Machine Learning

Part of the book series: The Springer Series on Challenges in Machine Learning ((SSCML))

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Abstract

This chapter addresses the problem of identifying the causal structure between two time-series processes. We focus on the setting typically encountered in econometrics, namely stationary or difference-stationary multiple autoregressive processes with additive white noise terms. We review different methods and algorithms, distinguishing between methods that filter the series through a vector autoregressive (VAR) model and methods that apply causal search directly to time series data. We also propose an additive noise model search algorithm tailored to the specific task of distinguishing among causal structures on time series pairs, under different assumptions, among which causal sufficiency.

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Notes

  1. 1.

    When referring to “causal relationships”, we endorse here, in the spirit of Hoover [32], Pearl [55], a structural account of causality: causal relationships are the fundamental, but usually latent, building blocks of the mechanism that has generate the observed data, which we aim at representing through a structural (or causal) model. While a structural model entails probabilistic relations, it contains more information than a statistical model, because it allows us to analyze the effect of interventions (cf. [58]).

  2. 2.

    Or, equivalently, the responses of Y t+i to forecast errors at time t.

  3. 3.

    A vertex i is an ancestor of j if there is a sequence of directed edges (→) between i and j. A vertex i is a parent of j if i → j. A vertex i is a spouse of j (and j a spouse of i) if there is a bi-directed edge between i and j.

  4. 4.

    Specific nonlinear functions f x(⋅) and distributions of the noise terms have also to be excluded. A precise specification can be found in Peters et al. [57, Proposition 23] and Zhang and Hyvärinen [69].

  5. 5.

    Here and below the subscript i in the function f i(⋅), as well as the superscript i in the noise term \(N_t^{\cdot ,i}\), indicate that these functions and noise terms enter in the additive noise model associated to DAG i (see Fig. 5.3).

References

  1. Ehung Baek and William Brock. A general test for nonlinear Granger causality: Bivariate model. Iowa State University and University of Wisconsin at Madison Working Paper, 1992.

    Google Scholar 

  2. David Bell, Jim Kay, and Jim Malley. A non-parametric approach to non-linear causality testing. Economics Letters, 51(1):7–18, 1996.

    Article  MATH  Google Scholar 

  3. David A Bessler and Seongpyo Lee. Money and prices: US data 1869–1914 (a study with directed graphs). Empirical Economics, 27(3):427–446, 2002.

    Article  Google Scholar 

  4. Taoufik Bouezmarni, Jeroen VK Rombouts, and Abderrahim Taamouti. Nonparametric copula-based test for conditional independence with applications to Granger causality. Journal of Business & Economic Statistics, 30(2):275–287, 2012.

    Article  MathSciNet  Google Scholar 

  5. Jean-François Cardoso and Antoine Souloumiac. Blind beamforming for non-Gaussian signals. In IEE proceedings F (radar and signal processing), volume 140, pages 362–370. IET, 1993.

    Google Scholar 

  6. Nadine Chlaß and Alessio Moneta. Can graphical causal inference be extended to nonlinear settings? In EPSA Epistemology and Methodology of Science, pages 63–72. Springer, 2009.

    Google Scholar 

  7. Tianjiao Chu and Clark Glymour. Search for additive nonlinear time series causal models. Journal of Machine Learning Research, 9(May):967–991, 2008.

    MathSciNet  MATH  Google Scholar 

  8. Diego Colombo, Marloes H Maathuis, Markus Kalisch, and Thomas S Richardson. Learning high-dimensional directed acyclic graphs with latent and selection variables. The Annals of Statistics, pages 294–321, 2012.

    Google Scholar 

  9. Pierre Comon. Independent component analysis, a new concept? Signal processing, 36(3):287–314, 1994.

    Article  MATH  Google Scholar 

  10. David Danks and Sergey Plis. Learning causal structure from undersampled time series. JMLR: Workshop and Conference Proceedings (NIPS Workshop on Causality), 2013.

    Google Scholar 

  11. Selva Demiralp and Kevin D Hoover. Searching for the causal structure of a vector autoregression. Oxford Bulletin of Economics and statistics, 65(s1):745–767, 2003.

    Article  Google Scholar 

  12. Cees Diks and Valentyn Panchenko. A new statistic and practical guidelines for nonparametric Granger causality testing. Journal of Economic Dynamics & Control, 30:1647–1669, 2006.

    Article  MathSciNet  MATH  Google Scholar 

  13. Michael Eichler. Causal inference in time series analysis. Causality: Statistical Perspectives and Applications, pages 327–354, 2012.

    Google Scholar 

  14. Doris Entner and Patrik O Hoyer. On causal discovery from time series data using FCI. Probabilistic graphical models, pages 121–128, 2010.

    Google Scholar 

  15. Jan Eriksson and Visa Koivunen. Identifiability, separability, and uniqueness of linear ICA models. IEEE signal processing letters, 11(7):601–604, 2004.

    Article  Google Scholar 

  16. Jean-Pierre Florens and Michel Mouchart. A note on noncausality. Econometrica, pages 583–591, 1982.

    Google Scholar 

  17. Claudia Foroni, Eric Ghysels, and Massimiliano Marcellino. Mixed-frequency vector autoregressive models. In VAR Models in Macroeconomics–New Developments and Applications: Essays in Honor of Christopher A. Sims, pages 247–272. Emerald Group Publishing Limited, 2013.

    Google Scholar 

  18. Andrea Gazzani and Alejandro Vicondoa. Proxy-svar as a bridge between mixed frequencies. Unpublished Manuscript, 2016.

    Google Scholar 

  19. John Geweke. Measurement of linear dependence and feedback between multiple time series. Journal of the American Statistical Association, 77(378):304–313, 1982.

    Article  MathSciNet  MATH  Google Scholar 

  20. Irving John Good. A causal calculus (i). The British Journal for the Philosophy of Science, 11(44):305–318, 1961a.

    Google Scholar 

  21. Irving John Good. A causal calculus (ii). The British Journal for the Philosophy of Science, 12(45):43–51, 1961b.

    Google Scholar 

  22. Christian Gouriéroux, Alain Monfort, and Jean-Paul Renne. Statistical inference for independent component analysis: Application to structural VAR models. Journal of Econometrics, 196(1):111–126, 2017.

    Article  MathSciNet  MATH  Google Scholar 

  23. Clive WJ Granger. Investigating causal relations by econometric models and cross-spectral methods. Econometrica, pages 424–438, 1969.

    Google Scholar 

  24. Clive WJ Granger. Testing for causality: a personal viewpoint. Journal of Economic Dynamics and control, 2:329–352, 1980.

    Google Scholar 

  25. Arthur Gretton, Kenji Fukumizu, Choon H Teo, Le Song, Bernhard Schölkopf, and Alex J Smola. A kernel statistical test of independence. In Advances in neural information processing systems, pages 585–592, 2008.

    Google Scholar 

  26. James Douglas Hamilton. Time Series Analysis, volume 2. Princeton university press Princeton, NJ, 1994.

    Google Scholar 

  27. Wolfgang Härdle, Helmut Lütkepohl, and Rong Chen. A review of nonparametric time series analysis. International Statistical Review, 65(1):49–72, 1997.

    Article  MATH  Google Scholar 

  28. Trevor Hastie and Rob Tibshirani. Independent components analysis through product density estimation. In Advances in neural information processing systems, pages 665–672, 2003.

    Google Scholar 

  29. David F Hendry. Dynamic Econometrics. Oxford University Press on Demand, 1995.

    Google Scholar 

  30. Helmut Herwartz. Hodges–Lehmann detection of structural shocks–an analysis of macroeconomic dynamics in the Euro area. Oxford Bulletin of Economics and Statistics, 2018.

    Google Scholar 

  31. Craig Hiemstra and Jonathan D Jones. Testing for linear and nonlinear Granger causality in the stock price-volume relation. The Journal of Finance, 49(5):1639–1664, 1994.

    Google Scholar 

  32. Kevin D Hoover. Causality in Macroeconomics. Cambridge University Press, 2001.

    Google Scholar 

  33. Kevin D Hoover. Economic theory and causal inference. In Uskali Mäki, editor, Philosophy of Economics. North Holland, 2012.

    Google Scholar 

  34. Patrik O Hoyer, Shohei Shimizu, Antti J Kerminen, and Markus Palviainen. Estimation of causal effects using linear non-gaussian causal models with hidden variables. International Journal of Approximate Reasoning, 49(2):362–378, 2008.

    Article  MathSciNet  MATH  Google Scholar 

  35. Patrik O Hoyer, Dominik Janzing, Joris M Mooij, Jonas Peters, and Bernhard Schölkopf. Nonlinear causal discovery with additive noise models. In Advances in neural information processing systems, pages 689–696, 2009.

    Google Scholar 

  36. Antti Hyttinen, Sergey Plis, Matti Järvisalo, Frederick Eberhardt, and David Danks. Causal discovery from subsampled time series data by constraint optimization. JMLR: Workshop and Conference Proceedings (PGM), 2016.

    Google Scholar 

  37. Aapo Hyvärinen. Independent component analysis: recent advances. Phil. Trans. R. Soc. A, 371(1984):20110534, 2013.

    Google Scholar 

  38. Aapo Hyvärinen and Erkki Oja. A fast fixed-point algorithm for independent component analysis. Neural computation, 9(7):1483–1492, 1997.

    Article  Google Scholar 

  39. Aapo Hyvärinen, Juha Karhunen, and Erkki Oja. Independent Component Analysis. Series on Adaptive and Learning Systems for Signal Processing, Communications, and Control. Wiley, 2001.

    Google Scholar 

  40. Aapo Hyvärinen, Kun Zhang, Shohei Shimizu, and Patrik O Hoyer. Estimation of a structural vector autoregression model using non-gaussianity. Journal of Machine Learning Research, 11(May):1709–1731, 2010.

    Google Scholar 

  41. Rodney L Jacobs, Edward E Leamer, and Michael P Ward. Difficulties with testing for causation. Economic Inquiry, 17(3):401–413, 1979.

    Article  Google Scholar 

  42. Oscar Jorda. Estimation and inference of impulse responses by local projections. American Economic Review, 95(1):161–182, 2005.

    Article  MathSciNet  Google Scholar 

  43. Maria Kalli and Jim E Griffin. Bayesian nonparametric vector autoregressive models. Journal of Econometrics, 203(2):267–282, 2018.

    Article  MathSciNet  MATH  Google Scholar 

  44. Lutz Kilian and Helmut Lütkepohl. Structural Vector Autoregressive Analysis. Cambridge University Press, 2017.

    Book  MATH  Google Scholar 

  45. Gary Koop, M Hashem Pesaran, and Simon M Potter. Impulse response analysis in nonlinear multivariate models. Journal of Econometrics, 74(1):119–147, 1996.

    Article  MathSciNet  MATH  Google Scholar 

  46. RJ Kulperger and RA Lockhart. Tests of independence in time series. Journal of Time Series Analysis, 19(2):165–185, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  47. Gustavo Lacerda, Peter L Spirtes, Joseph Ramsey, and Patrik O Hoyer. Discovering cyclic causal models by independent components analysis. In Proc. Conf. on Uncertainty in Artificial Intelligence (UAI-08), pages 366–374, 2008.

    Google Scholar 

  48. Markku Lanne, Mika Meitz, and Pentti Saikkonen. Identification and estimation of non-gaussian structural vector autoregressions. Journal of Econometrics, 196(2):288–304, 2017.

    Article  MathSciNet  MATH  Google Scholar 

  49. Helmut Lütkepohl. Vector autoregressive models. In Nigar Hashimzade and Michael A. Thornton, editors, Handbook of Research Methods and Applications in Empirical Macroeconomics, pages 139–164. Edward Elgar, 2013.

    Google Scholar 

  50. Massimiliano Marcellino. Some consequences of temporal aggregation in empirical analysis. Journal of Business & Economic Statistics, 17(1):129–136, 1999.

    MathSciNet  Google Scholar 

  51. David S Matteson and Ruey S Tsay. Independent component analysis via distance covariance. Journal of the American Statistical Association, 112(518):623–637, 2017.

    Article  MathSciNet  Google Scholar 

  52. Alessio Moneta. Graphical causal models and vars: an empirical assessment of the real business cycles hypothesis. Empirical Economics, 35(2):275–300, 2008.

    Article  Google Scholar 

  53. Alessio Moneta, Doris Entner, Patrik O Hoyer, and Alex Coad. Causal inference by independent component analysis: Theory and applications. Oxford Bulletin of Economics and Statistics, 75(5):705–730, 2013.

    Google Scholar 

  54. Judea Pearl. Probabilistic reasoning in intelligent systems: Networks of plausible reasoning. Morgan Kaufmann Publishers, Los Altos, 1988.

    MATH  Google Scholar 

  55. Judea Pearl. Causality: Models, Reasoning, and Inference. Cambridge University Press, 2009.

    Book  MATH  Google Scholar 

  56. Jonas Peters, Dominik Janzing, and Bernhard Schölkopf. Causal inference on time series using restricted structural equation models. In Advances in Neural Information Processing Systems, pages 154–162, 2013.

    Google Scholar 

  57. Jonas Peters, Joris M Mooij, Dominik Janzing, and Bernhard Schölkopf. Causal discovery with continuous additive noise models. The Journal of Machine Learning Research, 15(1):2009–2053, 2014.

    Google Scholar 

  58. Jonas Peters, Dominik Janzing, and Bernhard Schölkopf. Elements of Causal Inference: Foundations and Learning Algorithms. MIT press, 2017.

    MATH  Google Scholar 

  59. Giorgio E Primiceri. Time varying structural vector autoregressions and monetary policy. The Review of Economic Studies, 72(3):821–852, 2005.

    Article  MathSciNet  MATH  Google Scholar 

  60. Thomas Richardson and Peter Spirtes. Ancestral graph markov models. The Annals of Statistics, 30(4):962–1030, 2002.

    Article  MathSciNet  MATH  Google Scholar 

  61. Shohei Shimizu, Patrik O. Hoyer, Aapo Hyvärinen, and Antti Kerminen. A linear non-Gaussian acyclic model for causal discovery. Journal of Machine Learning Research, 7:2003–2030, 2006.

    MathSciNet  MATH  Google Scholar 

  62. Christopher A Sims. Macroeconomics and reality. Econometrica, pages 1–48, 1980.

    Google Scholar 

  63. Peter Spirtes and Kun Zhang. Causal discovery and inference: concepts and recent methodological advances. In Applied informatics, volume 3, page 3. SpringerOpen, 2016.

    Google Scholar 

  64. Peter Spirtes, Clark N Glymour, and Richard Scheines. Causation, Prediction, and Search. MIT press, 2000.

    Google Scholar 

  65. Wolfgang Spohn. Probabilistic causality: From Hume via Suppes to Granger. In M. Galvotti and G. Gambetta, editors, Causalità e modelli probabilistici, pages 69–87. Clueb, 1983.

    Google Scholar 

  66. Liangjun Su and Halbert White. A nonparametric Hellinger metric test for conditional independence. Econometric Theory, 24(4):829–864, 2008.

    Article  MathSciNet  MATH  Google Scholar 

  67. Patrick Suppes. A probabilistic theory of causality. North-Holland, Amsterdam, 1970.

    Google Scholar 

  68. Norman R Swanson and Clive WJ Granger. Impulse response functions based on a causal approach to residual orthogonalization in vector autoregressions. Journal of the American Statistical Association, 92(437):357–367, 1997.

    Article  MathSciNet  MATH  Google Scholar 

  69. Kun Zhang and Aapo Hyvärinen. On the identifiability of the post-nonlinear causal model. In Proceedings of the twenty-fifth conference on uncertainty in artificial intelligence, pages 647–655. AUAI Press, 2009.

    Google Scholar 

  70. Kun Zhang, Jonas Peters, Dominik Janzing, and Bernhard Schölkopf. Kernel-based conditional independence test and application in causal discovery. In Proceedings of the Twenty-Seventh Conference on Uncertainty in Artificial Intelligence, pages 804–813. AUAI Press, 2011.

    Google Scholar 

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Acknowledgements

The authors want to thank Isabelle Guyon, Alexander Statnikov, and Daniele Marinazzo for very valuable comments on a first draft.

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Authors and Affiliations

  1. IUSS Pavia, Pavia, Italy

    Nicolas Doremus

  2. Sant’Anna School of Advanced Studies, Pisa, Italy

    Alessio Moneta

  3. Rovira i Virgili University, Tarragona, Spain

    Sebastiano Cattaruzzo

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  1. Nicolas Doremus
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  2. Alessio Moneta
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  3. Sebastiano Cattaruzzo
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Correspondence to Nicolas Doremus .

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Editors and Affiliations

  1. Team TAU - CNRS, INRIA, Université Paris Sud, Université Paris Saclay, Orsay France, ChaLearn, Berkeley, CA, USA

    Isabelle Guyon

  2. SoFi, San Francisco, CA, USA

    Alexander Statnikov

  3. University of Paris-Sud, Paris-Saclay, Paris, France

    Berna Bakir Batu

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Doremus, N., Moneta, A., Cattaruzzo, S. (2019). Cause-Effect Pairs in Time Series with a Focus on Econometrics. In: Guyon, I., Statnikov, A., Batu, B. (eds) Cause Effect Pairs in Machine Learning. The Springer Series on Challenges in Machine Learning. Springer, Cham. https://doi.org/10.1007/978-3-030-21810-2_5

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