Stationary Processes, Wiener-Granger Causality, and Matrix Spectral Factorization

TL;DR

This paper reviews the mathematical foundations and historical development of Granger causality, discusses recent computational improvements, and explores future directions for large-scale data analysis in causal inference.

Contribution

It provides a comprehensive overview of Granger causality, including proofs, historical context, and potential future research avenues, especially for large datasets.

Findings

Enhanced computational methods for Granger causality

Historical analysis of causality concepts

Future research directions in large-scale data

Abstract

Granger causality has become an indispensable tool for analyzing causal relationships between time series. In this paper, we provide a detailed overview of its mathematical foundations, trace its historical development, and explore how recent computational advancements can enhance its application in various fields. We will not hesitate to present the proofs in full if they are simple and transparent. For more complex theorems on which we rely, we will provide supporting citations. We also discuss potential future directions for the method, particularly in the context of largescale data analysis.