Extremes of multivariate ARMAX processes

TL;DR

This paper introduces a multivariate ARMAX process, explores its extremal properties, and proposes new methods for constructing multivariate extreme value copulas and estimating key parameters.

Contribution

It generalizes the ARMAX process to multivariate settings, providing new theoretical insights and estimation techniques for extremal dependence and parameters.

Findings

Derived conditions for stationarity of the multivariate ARMAX process

Developed a new method for constructing multivariate extreme value copulas

Proposed estimators for the multivariate extremal index and ARMAX parameters

Abstract

We define a new multivariate time series model by generalizing the ARMAX process in a multivariate way. We give conditions on stationarity and analyze local dependence and domains of attraction. As a consequence of the obtained result, we derive a new method of construction of multivariate extreme value copulas. We characterize the extremal dependence by computing the multivariate extremal index and bivariate upper tail dependence coefficients. An estimation procedure for the multivariate extremal index shall be presented. We also address the marginal estimation and propose a new estimator for the ARMAX autoregressive parameter.