Generalized moment estimators for \(\alpha\)-stable Ornstein-Uhlenbeck motions from discrete observations
type: Item
instance of: scholarly article
title: Generalized moment estimators for \(\alpha\)-stable Ornstein-Uhlenbeck motions from discrete observations
zbMATH Open document ID: 1436.62084
author: Yiying Cheng
author: Hongwei Long
author: Yaozhong Hu
published in: Statistical Inference for Stochastic Processes
publication date: 2020-04-07T00:00:00Z
review text: The authors study the parameter estimation problem for discretely observed Ornstein-Uhlenbeck processes driven by \(\alpha\)-stable Lévy motions. The \(\alpha\)-stable Lévy motions is a stochastic process \((Z_t,t\geq 0)\) for which \(Z_1\in S_{\alpha}(1,\beta,0)\) where \(\alpha\) is the index of stablility and \(\beta\in(-1,1)\) is the skewness. Then Ornstein-Uhlenbeck processes driven by the \(\alpha\)-stable Lévy motion \(Z_t\) is presented by the stochastic equation \(dX_t=-\theta X_tdt+\sigma dZ_t,\; t\in[0,\infty),\;X_0=x_0,\) where \(\theta\), \(\sigma\) are some constants. If \(\theta>0,\) \(X_t\) is ergodic and it converges in law to the random variable \(X_0=\sigma\int_0^{\infty} e^{-\theta s}dZ_s.\) A method of moments via ergodic theory and via sample characteristic functions is proposed to estimate all the parameters involved in the Ornstein-Uhlenbeck processes. The strong consistency and the asymptotic normality of the proposed joint estimators when \(n \rightarrow \infty\) are demonstrated.
reviewed by: Pavel Stoynov
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 62M05
Mathematics Subject Classification ID: 60G52
Mathematics Subject Classification ID: 60G65
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 7186885
zbMATH Keywords: \(\alpha\)-stable Ornstein-Uhlenbeck motions
zbMATH Keywords: discrete time observation
zbMATH Keywords: characteristic functions
zbMATH Keywords: generalized moment estimators
zbMATH Keywords: consistency
zbMATH Keywords: asymptotic normality
MaRDI profile type: Publication
full work available at URL: s11203-019-09201-4
OpenAlex ID: W2953588946
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DOI: 10.1007/S11203-019-09201-4
description: scientific article; zbMATH DE number 7186885