# Identifiability and Estimation of Structural Vector Autoregressive Models for Subsampled and Mixed Frequency Time Series

## TL;DR

This paper develops a unifying framework for identifying and estimating causal relationships in multivariate time series observed at different sampling rates, using non-Gaussian SVAR models and an EM algorithm.

## Contribution

It introduces a novel approach for causal inference in subsampled and mixed frequency time series using non-Gaussian SVAR models, with new identifiability and estimation methods.

## Key findings

- Successfully validated on simulated data
- Effective in real-world datasets
- Provides exact EM algorithm for inference

## 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.