Title: Properties and Estimation of GARCH(1,1) Model
Abstract: 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 condition al 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 bounded conditional fourth moment of the rescaled variable (the ratio of the disturbance to the condi tional standard deviation) is sufficient for the result. Consistent estimation and asympt otic normality are demonstrated, as well as consistent estimation of the asymptotic covariance matrix.
Publication Year: 2005
Publication Date: 2005-01-01
Language: en
Type: article
Access and Citation
Cited By Count: 23
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot