Premium
Structure and estimation of a class of nonstationary yet nonexplosive GARCH models
Author(s) -
Regnard Nazim,
Zakoïan JeanMichel
Publication year - 2010
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2010.00669.x
Subject(s) - mathematics , estimator , autoregressive conditional heteroskedasticity , series (stratigraphy) , econometrics , class (philosophy) , estimation , maximum likelihood , statistics , economics , computer science , artificial intelligence , volatility (finance) , management , paleontology , biology
This article considers GARCH(1,1) models in which the time‐varying coefficients are functions of the realizations of an exogenous stochastic process. Time series generated by this model are in general nonstationary. Necessary and sufficient conditions are given for the existence of nonexplosive solutions, and for the existence of moments of these solutions. The asymptotic properties of the quasi‐maximum likelihood estimator are derived under mild assumptions.