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A survey of recent theoretical results for time series models with GARCH errors

Li, Wai Keung (contributor); Ling, Shiqing (contributor); … - 2001 - [Elektronische Ressource]

directed towards practitioners. Starting with the simple ARCH model and proceeding to the GARCH model, some results for … stationary and nonstationary ARMA-GARCH are summarized. Various new ARCH-type models, including double threshold ARCH and GARCH …

Persistent link: https://www.econbiz.de/10001644062

Necessary and sufficient moment conditions for the GARCH(r,s) and asymmetric power GARCH(r,s) models

Ling, Shiqing (contributor); McAleer, Michael (contributor) - 2001 - [Elektronische Ressource]

Although econometricians have been using Bollerslev’s (1986) GARCH (r, s) model for over a decade, the higher-order moment structure of the model remains unresolved. The sufficient condition for the existence of the higherorder moments of the GARCH (r, s) model was given by Ling (1999a). This...

Persistent link: https://www.econbiz.de/10001644071

Stationarity and the existence of moments of a family of GARCH processes

Ling, Shiqing (contributor); McAleer, Michael (contributor) - 2001 - [Elektronische Ressource]

This paper investigates some structural properties of a family of GARCH processes. A simple sufficient condition for the existence of the αδ-order stationary solution of the processes is derived, where α ∈ (0, 1] and δ 0. The solution is strictly stationary and ergodic, and the causal...

Persistent link: https://www.econbiz.de/10001644082

Asymptotic theory for a vector ARMA-GARCH model

Ling, Shiqing (contributor); McAleer, Michael (contributor) - 2001 - [Elektronische Ressource]

(QMLE) is proved under only the second-order moment condition. This consistency result is new, even for the univariate ARCH … and GARCH models. Moreover, the asymptotic normality of the QMLE for the vector ARCH model is obtained under only the … additional moment conditions, the asymptotic normality of the QMLE is also obtained for the vector ARMA-ARCH and ARMA …

Persistent link: https://www.econbiz.de/10001644276

On adaptive estimation in nonstationary ARMA models with GARCH errors

Ling, Shiqing (contributor); McAleer, Michael (contributor) - 2001 - [Elektronische Ressource]

This paper considers adaptive estimation in nonstationary autoregressive moving average models with the noise sequence satisfying a generalised autoregressive conditional heteroscedastic process. The locally asymptotic quadratic form of the log-likelihood ratio for the model is obtained. It is...

Persistent link: https://www.econbiz.de/10001644277

Estimating smooth transition autoregressive models with GARCH errors in the presence of extreme observations and outliers

Chan, Felix (contributor); McAleer, Michael (contributor) - 2001 - [Elektronische Ressource]

This paper investigates several empirical issues regarding quasimaximum likelihood estimation of Smooth Transition Autoregressive (STAR) models with GARCH errors, specifically STAR-GARCH and STAR-STGARCH. Convergence, the choice of different algorithms for maximising the likelihood function, and...

Persistent link: https://www.econbiz.de/10001644307