  Causal inference from observational data following the restricted structural
causal model (SCM) framework hinges largely on the asymmetry between cause and
effect from the data generating mechanisms, such as non-Gaussianity or
nonlinearity. This methodology can be adapted to stationary time series, yet
inferring causal relationships from nonstationary time series remains a
challenging task. In this work, we propose a new class of restricted SCM, via a
time-varying filter and stationary noise, and exploit the asymmetry from
nonstationarity for causal identification in both bivariate and network
settings. We propose efficient procedures by leveraging powerful estimates of
the bivariate evolutionary spectra for slowly varying processes. Various
synthetic and real datasets that involve high-order and non-smooth filters are
evaluated to demonstrate the effectiveness of our proposed methodology.
