  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.
