Mitigating the effects of measurement noise on Granger causality

TL;DR

This paper analyzes how measurement noise affects Granger causality estimation in time series and proposes a Kalman filter and EM algorithm-based denoising method to improve accuracy.

Contribution

It provides an analytical and numerical study of noise effects on Granger causality and introduces a novel denoising algorithm to mitigate these issues.

Findings

Noise can cause spurious causality detection.

True causality can be suppressed by noise.

The proposed denoising method effectively improves causality estimation.

Abstract

Computing Granger causal relations among bivariate experimentally observed time series has received increasing attention over the past few years. Such causal relations, if correctly estimated, can yield significant insights into the dynamical organization of the system being investigated. Since experimental measurements are inevitably contaminated by noise, it is thus important to understand the effects of such noise on Granger causality estimation. The first goal of this paper is to provide an analytical and numerical analysis of this problem. Specifically, we show that, due to noise contamination, (1) spurious causality between two measured variables can arise and (2) true causality can be suppressed. The second goal of the paper is to provide a denoising strategy to mitigate this problem. Specifically, we propose a denoising algorithm based on the combined use of the Kalman filter theory and the Expectation-Maximization (EM) algorithm. Numerical examples are used to demonstrate the effectiveness of the denoising approach.