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2018

Structural causal models for macro-variables in time-series

Janzing, Dominik, Rubenstein, Paul, Schölkopf, Bernhard

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We consider a bivariate time series $(X_t,Y_t)$ that is given by a simple linear autoregressive model.

Assuming that the equations describing each variable as a linear combination of past values are considered structural equations, there is a clear meaning of how intervening on one particular $X_t$ influences $Y_{t'}$ at later times $t'>t$.
In the present work, we describe conditions under which one can define a causal model between variables that are coarse-grained in time, thus admitting statements like `setting $X$ to $x$ changes $Y$ in a certain way' without referring to specific time instances.
We show that particularly simple statements follow in the frequency domain, thus providing meaning to interventions on frequencies.

Structural causal models for macro-variables in time-series · Around

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Investigating causal relations by econometric models and cross-spectral methods
C. W. J. Granger · 1969
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Directed cyclic graphical representations of feedback models
P. Spirtes · 1995
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Markov properties of nonrecursive causal models
J. T. A. Koster · 1996
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Identifying independence in causal graphs with feedback
J. Pearl and R. Dechter · 1996
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Causality
J. Pearl · 2000
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Causal interpretation of stochastic differential equations
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From deterministic ODEs to dynamic structural causal models
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Causal consistency of structural equation models
Original
P. K. Rubenstein, S. Weichwald, S. Bongers, J. M. Mooij, D. Janzing, M. Grosse-Wentrup, and B. Schölkopf · 2017
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