Title: Identifiability and Estimation of Structural Vector Autoregressive Models for Subsampled and Mixed Frequency Time Series,
Abstract: Causal inference in multivariate time series is challenging due to the fact
that the sampling rate may not be as fast as the timescale of the causal
interactions. In this context, we can view our observed series as a subsampled
version of the desired series. Furthermore, due to technological and other
limitations, series may be observed at different sampling rates, representing a
mixed frequency setting. To determine instantaneous and lagged effects between
time series at the true causal scale, we take a model-based approach based on
structural vector autoregressive (SVAR) models. In this context, we present a
unifying framework for parameter identifiability and estimation under both
subsampling and mixed frequencies when the noise, or shocks, are non-Gaussian.
Importantly, by studying the SVAR case, we are able to both provide
identifiability and estimation methods for the causal structure of both lagged
and instantaneous effects at the desired time scale. We further derive an exact
EM algorithm for inference in both subsampled and mixed frequency settings. We
validate our approach in simulated scenarios and on two real world data sets.