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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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1549681240

Digital Object Identifier
doi:10.1214/18-EJS1523

Subjects
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

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

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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