A closed-form estimator for the multivariate GARCH(1,1) model

TL;DR

This paper introduces a closed-form estimator for the multivariate GARCH(1,1) model, enabling straightforward parameter estimation using linear algebra, with proven consistency and asymptotic normality.

Contribution

It presents a novel closed-form estimator for multivariate GARCH(1,1) based on VARMA representation, simplifying parameter estimation and analysis.

Findings

Estimator is consistent and asymptotically normal.

Allows derivation of parameters under temporal aggregation.

Provides a linear algebra-based solution for GARCH(1,1) parameters.

Abstract

We provide a closed-form estimator based on the VARMA representation for the unrestricted multivariate GARCH(1,1). We show that all parameters can be derived using basic linear algebra tools. We show that the estimator is consistent and asymptotically normal distributed. Our results allow also to derive a closed form for the parameters in the context of temporal aggregation of multivariate GARCH(1,1) by solving the equations as in Hafner [2008].