  Inferring causation from time series data is of scientific interest in
different disciplines, particularly in neural connectomics. While different
approaches exist in the literature with parametric modeling assumptions, we
focus on a non-parametric model for time series satisfying a Markovian
structural causal model with stationary distribution and without concurrent
effects. We show that the model structure can be used to its advantage to
obtain an elegant algorithm for causal inference from time series based on
conditional dependence tests, coined Causal Inference in Time Series (CITS)
algorithm. We describe Pearson's partial correlation and Hilbert-Schmidt
criterion as candidates for such conditional dependence tests that can be used
in CITS for the Gaussian and non-Gaussian settings, respectively. We prove the
mathematical guarantee of the CITS algorithm in recovering the true causal
graph, under standard mixing conditions on the underlying time series. We also
conduct a comparative evaluation of performance of CITS with other existing
methodologies in simulated datasets. We then describe the utlity of the
methodology in neural connectomics -- in inferring causal functional
connectivity from time series of neural activity, and demonstrate its
application to a real neurobiological dataset of electro-physiological
recordings from the mouse visual cortex recorded by Neuropixel probes.
