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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).

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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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  • DOI: https://doi.org/10.1007/978-3-030-21810-2_5

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