Moment based estimation for the multivariate COGARCH(1,1) process

TL;DR

This paper develops a moment-based estimation method for the multivariate COGARCH(1,1) process, providing explicit second-order structure expressions, proving consistency and asymptotic normality of the estimator, and validating it through simulations.

Contribution

It introduces a generalized method of moments estimator for the multivariate COGARCH(1,1) process with proven statistical properties and detailed conditions for model assumptions.

Findings

Estimator is consistent and asymptotically normal.

Explicit second-order structure expressions derived.

Simulation study confirms finite sample performance.

Abstract

For the multivariate COGARCH process, we obtain explicit expressions for the second-order structure of the "squared returns" process observed on an equidistant grid. Based on this, we present a generalized method of moments estimator for its parameters. Under appropriate moment and strong mixing conditions, we show that the resulting estimator is consistent and asymptotically normal. Sufficient conditions for strong mixing, stationarity and identifiability of the model parameters are discussed in detail. We investigate the finite sample behavior of the estimator in a simulation study.