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2009 Statistical inference for non-stationary GARCH(p,q) models
Ngai Hang Chan, Chi Tim Ng
Electron. J. Statist. 3: 956-992 (2009). DOI: 10.1214/09-EJS452

Abstract

This paper studies the quasi-maximum likelihood estimator (QMLE) of non-stationary GARCH(p,q) models. By expressing GARCH models in matrix form, the log-likelihood function is written in terms of the product of random matrices. Oseledec’s multiplicative ergodic theorem is then used to establish the asymptotic properties of the log-likelihood function and thereby, showing the weak consistency and the asymptotic normality of the QMLE for non-stationary GARCH(p,q) models.

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Ngai Hang Chan. Chi Tim Ng. "Statistical inference for non-stationary GARCH(p,q) models." Electron. J. Statist. 3 956 - 992, 2009. https://doi.org/10.1214/09-EJS452

Information

Published: 2009
First available in Project Euclid: 17 September 2009

zbMATH: 1326.62184
MathSciNet: MR2540848
Digital Object Identifier: 10.1214/09-EJS452

Subjects:
Primary: 62G30
Secondary: 62M10

Keywords: asymptotic normality , consistency , non-stationary GARCH model , Oseledec’s multiplicative ergodic theorem , Product of random matrices , quasi-maximum likelihood estimator

Rights: Copyright © 2009 The Institute of Mathematical Statistics and the Bernoulli Society

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