Properties and estimation of garch(1,1) model

Posedel, Petra (author)

We study in depth the properties of the GARCH(1,1) model and the assumptions on the parameter space under which the process is stationary. In particular, we prove ergodicity and strong stationarity for the conditional variance (squared volatility) of the process. We show under which conditions higher order moments of the GARCH(1,1) process exist and conclude that GARCH processes are heavy-tailed. We investigate the sampling behavior of the quasi-maximum likelihood estimator of the Gaussian GARCH(1,1) model. A boundedconditional fourth moment of the rescaled variable (the ratio of the disturbance to the conditional standard deviation) is sufficient for the result. Consistent estimation and asymptotic normality are demonstrated, as well as consistent estimation of the asymptotic covariance matrix.

• Language: English
• Work type: Not categorized
• Typology: 1.01 - Original Scientific Article
• Organization: FDV - Faculty of Social Sciences
• Year: 2005
• Number of pages: Str. 243-257
• Numbering: no. 2
• PID: 20.500.12556/RUL-22455
• UDC: 303
• ISSN on article: 1854-0023
• COBISS.SI-ID: 24315997
• Publication date in RUL: 11.07.2014

POSEDEL, Petra, 2005, Properties and estimation of garch(1,1) model. Advances in methodology and statistics [online]. 2005. Vol. 2, p. 243–257. [Accessed 17 April 2025]. Retrieved from: http://mrvar.fdv.uni-lj.si/pub/mz/mz2.1/posedel.pdf

Record is a part of a journal

• Title: Advances in methodology and statistics
• Shortened title: Metodol. zv.
• Publisher: Fakulteta za družbene vede
• ISSN: 1854-0023
• COBISS.SI-ID: 215795712