Electronic Journal of Statistics

Statistical inference for non-stationary GARCH(p,q) models

Ngai Hang Chan and Chi Tim Ng

Full-text: Open access

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.

Article information

Source
Electron. J. Statist., Volume 3 (2009), 956-992.

Dates
First available in Project Euclid: 17 September 2009

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1253195941

Digital Object Identifier
doi:10.1214/09-EJS452

Mathematical Reviews number (MathSciNet)
MR2540848

Zentralblatt MATH identifier
1326.62184

Subjects
Primary: 62G30: Order statistics; empirical distribution functions
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

Keywords
Asymptotic normality consistency non-stationary GARCH model Oseledec’s multiplicative ergodic theorem product of random matrices quasi-maximum likelihood estimator

Citation

Chan, Ngai Hang; Ng, Chi Tim. Statistical inference for non-stationary GARCH( p , q ) models. Electron. J. Statist. 3 (2009), 956--992. doi:10.1214/09-EJS452. https://projecteuclid.org/euclid.ejs/1253195941


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