Weak dependence and GMM estimation of supOU and mixed moving average processes

TL;DR

This paper studies the weak dependence properties of MMA and supOU processes driven by Lévy bases, establishing conditions for normal limit theorems, and analyzes GMM estimators for these models and their stochastic volatility extensions.

Contribution

It introduces new weak dependence rates for MMA processes and extends GMM estimation techniques to supOU and supOU stochastic volatility models.

Findings

Weak dependence rates are derived for MMA processes.

Conditions for asymptotic normality of sample mean and autocovariances.

Asymptotic analysis of GMM estimators for supOU models.

Abstract

We consider a mixed moving average (MMA) process X driven by a L\'evy basis and prove that it is weakly dependent with rates computable in terms of the moving average kernel and the characteristic quadruple of the L\'evy basis. Using this property, we show conditions ensuring that sample mean and autocovariances of X have a limiting normal distribution. We extend these results to stochastic volatility models and then investigate a Generalized Method of Moments estimator for the supOU process and the supOU stochastic volatility model after choosing a suitable distribution for the mean reversion parameter. For these estimators, we analyze the asymptotic behavior in detail.