Causal Inference on Time Series using Structural Equation Models
This work addresses causal inference for time series data, which is incremental as it builds on traditional methods like Granger causality by introducing new model assumptions and algorithms.
The paper tackles the problem of causal inference in time series by introducing TiMINo models that require independent residual time series, and it results in a more general identifiability theory and an algorithm that outperforms existing methods on artificial and real data.
Causal inference uses observations to infer the causal structure of the data generating system. We study a class of functional models that we call Time Series Models with Independent Noise (TiMINo). These models require independent residual time series, whereas traditional methods like Granger causality exploit the variance of residuals. There are two main contributions: (1) Theoretical: By restricting the model class (e.g. to additive noise) we can provide a more general identifiability result than existing ones. This result incorporates lagged and instantaneous effects that can be nonlinear and do not need to be faithful, and non-instantaneous feedbacks between the time series. (2) Practical: If there are no feedback loops between time series, we propose an algorithm based on non-linear independence tests of time series. When the data are causally insufficient, or the data generating process does not satisfy the model assumptions, this algorithm may still give partial results, but mostly avoids incorrect answers. An extension to (non-instantaneous) feedbacks is possible, but not discussed. It outperforms existing methods on artificial and real data. Code can be provided upon request.