Direct estimation of differential Granger causality between two high-dimensional time series

TL;DR

This paper introduces a new method for directly estimating the differences in Granger causality between two high-dimensional time series, improving efficiency and support recovery by focusing on the difference rather than individual models.

Contribution

The paper proposes a novel direct estimation approach for differential Granger causality that leverages the difference in transition matrices, allowing for high-dimensional analysis with sparsity assumptions.

Findings

Method is consistent in estimation and support recovery.

Simulation studies demonstrate good finite sample performance.

Application to EEG data shows practical utility.

Abstract

Differential Granger causality, that is understanding how Granger causal relations differ between two related time series, is of interest in many scientific applications. Modeling each time series by a vector autoregressive (VAR) model, we propose a new method to directly learn the difference between the corresponding transition matrices in high dimensions. Key to the new method is an estimating equation constructed based on the Yule-Walker equation that links the difference in transition matrices to the difference in the corresponding precision matrices. In contrast to separately estimating each transition matrix and then calculating the difference, the proposed direct estimation method only requires sparsity of the difference of the two VAR models, and hence allows hub nodes in each high-dimensional time series. The direct estimator is shown to be consistent in estimation and support recovery under mild assumptions. These results also lead to novel consistency results with potentially faster convergence rates for estimating differences between precision matrices of i.i.d observations under weaker assumptions than existing results. We evaluate the finite sample performance of the proposed method using simulation studies and an application to electroencephalogram (EEG) data.