Structural causal models for macro-variables in time-series

2018/04/11 by Dominik Janzing, Paul K. Rubenstein, Janzing, Dominik +4 · 2 citations
Chemistry · Computer Science · Mathematics · #Blind Source Separation Techniques #Molecular spectroscopy and chirality #Neural Networks and Applications #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1804.03911

8 pages

arxiv created 2018/04/11 · arxiv updated 2018/04/12

Abstract

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.

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• Causality and Generalizability: Identifiability and Learning Methods
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