Yule-Walker Equations Using a Gini Covariance Matrix for the High-Dimensional Heavy-Tailed PVAR Model

Gini covariance plays a vital role in analyzing the relationship between random variables with heavy-tailed distributions. In this papaer, with the existence of a finite second moment, we establish the Gini-Yule-Walker equation to estimate the transition matrix of high-dimensional periodic vector autoregressive (PVAR) processes, the asymptotic results of estimators have been established. We apply this method to study the Granger causality of the heavy-tailed PVAR process, and the results show that the robust transfer matrix estimation induces sign consistency in the value of Granger causality. Effectiveness of the proposed method is verified by both synthetic and real data.

Automated summary

This paper focuses on the vital role of Gini covariance in analyzing the relationship between random variables with heavy-tailed distributions. The authors establish the Gini-Yule-Walker equation to estimate the transition matrix of high-dimensional periodic vector autoregressive processes, and apply this method to study the Granger causality of heavy-tailed PVAR processes, with results showing robust transfer matrix estimation leads to sign consistency in the value of Granger causality. The effectiveness of the proposed method is verified through both synthetic and real data.