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

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