Electronic Journal of Statistics

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

Imma Valentina Curato and Robert Stelzer

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We consider a mixed moving average (MMA) process $X$ driven by a Lévy basis and prove that it is weakly dependent with rates computable in terms of the moving average kernel and the characteristic quadruple of the Lévy 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.

Article information

Electron. J. Statist., Volume 13, Number 1 (2019), 310-360.

Received: July 2018
First available in Project Euclid: 9 February 2019

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Primary: 60E07: Infinitely divisible distributions; stable distributions 60G10: Stationary processes 60G51: Processes with independent increments; Lévy processes 60G57: Random measures
Secondary: 62F12: Asymptotic properties of estimators

Weak dependence Lévy basis generalized method of moments Ornstein-Uhlenbeck type process stochastic volatility

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Curato, Imma Valentina; Stelzer, Robert. Weak dependence and GMM estimation of supOU and mixed moving average processes. Electron. J. Statist. 13 (2019), no. 1, 310--360. doi:10.1214/18-EJS1523. https://projecteuclid.org/euclid.ejs/1549681240

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