Granger Causality: A Review and Recent Advances

TL;DR

This paper reviews the history, debates, and recent advances in Granger causality, highlighting developments that extend its applicability to high-dimensional, nonlinear, and mixed frequency time series data.

Contribution

It provides a comprehensive review of Granger causality and discusses recent methodological advances that overcome previous limitations in its application.

Findings

Recent models handle high-dimensional data effectively.

Advances incorporate nonlinear and non-Gaussian observations.

New methods enable analysis of sub-sampled and mixed frequency series.

Abstract

Introduced more than a half century ago, Granger causality has become a popular tool for analyzing time series data in many application domains, from economics and finance to genomics and neuroscience. Despite this popularity, the validity of this notion for inferring causal relationships among time series has remained the topic of continuous debate. Moreover, while the original definition was general, limitations in computational tools have primarily limited the applications of Granger causality to simple bivariate vector auto-regressive processes or pairwise relationships among a set of variables. Starting with a review of early developments and debates, this paper discusses recent advances that address various shortcomings of the earlier approaches, from models for high-dimensional time series to more recent developments that account for nonlinear and non-Gaussian observations and allow for sub-sampled and mixed frequency time series.