QUASI-MAXIMUM LIKELIHOOD ESTIMATION OF SEMI-STRONG GARCH MODELS

2009 ◽  
Vol 25 (2) ◽  
pp. 561-570 ◽  
Author(s):  
Juan Carlos Escanciano
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Garch Models ◽  
Martingale Difference ◽  
Likelihood Estimator ◽  
Conditional Mean ◽  
Mild Conditions ◽  
Consistency And Asymptotic Normality ◽  
Quasi Maximum Likelihood

This note proves the consistency and asymptotic normality of the quasi–maximum likelihood estimator (QMLE) of the parameters of a generalized autoregressive conditional heteroskedastic (GARCH) model with martingale difference centered squared innovations. The results are obtained under mild conditions and generalize and improve those in Lee and Hansen (1994,Econometric Theory10, 29–52) for the local QMLE in semistrong GARCH(1,1) models. In particular, no restrictions on the conditional mean are imposed. Our proofs closely follow those in Francq and Zakoïan (2004,Bernoulli10, 605–637) for independent and identically distributed innovations.

scholarly journals Identifying Stabilising Effects on Survey Based Life Satisfaction Using Quasi-maximum Likelihood Estimation

2021 ◽  
Author(s):  
Johannes Klement
Keyword(s):  
Life Satisfaction ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Negative Binomial ◽  
Measurement Instrument ◽  
Likelihood Estimation ◽  
Satisfaction Scale ◽  
Quasi Maximum Likelihood ◽  
The Stability

AbstractTo which extent do happiness correlates contribute to the stability of life satisfaction? Which method is appropriate to provide a conclusive answer to this question? Based on life satisfaction data of the German SOEP, we show that by Negative Binomial quasi-maximum likelihood estimation statements can be made as to how far correlates of happiness contribute to the stabilisation of life satisfaction. The results show that happiness correlates which are generally associated with a positive change in life satisfaction, also stabilise life satisfaction and destabilise dissatisfaction with life. In such as they lower the probability of leaving positive states of life satisfaction and increase the probability of leaving dissatisfied states. This in particular applies to regular exercise, volunteering and living in a marriage. We further conclude that both patterns in response behaviour and the quality of the measurement instrument, the life satisfaction scale, have a significant effect on the variation and stability of reported life satisfaction.

scholarly journals PARAMETER ESTIMATION IN NONLINEAR AR–GARCH MODELS

2011 ◽  
Vol 27 (6) ◽  
pp. 1236-1278 ◽  
Author(s):  
Mika Meitz ◽  
Pentti Saikkonen
Keyword(s):  
Asymptotic Normality ◽  
Autoregressive Models ◽  
Garch Models ◽  
Martingale Difference ◽  
First Order ◽  
First Results ◽  
Consistency And Asymptotic Normality ◽  
Quasi Maximum Likelihood ◽  
Nonlinear Autoregressive ◽  
Nonlinear Autoregressive Models

This paper develops an asymptotic estimation theory for nonlinear autoregressive models with conditionally heteroskedastic errors. We consider a general nonlinear autoregression of order p (AR(p)) with the conditional variance specified as a general nonlinear first-order generalized autoregressive conditional heteroskedasticity (GARCH(1,1)) model. We do not require the rescaled errors to be independent, but instead only to form a stationary and ergodic martingale difference sequence. Strong consistency and asymptotic normality of the global Gaussian quasi-maximum likelihood (QML) estimator are established under conditions comparable to those recently used in the corresponding linear case. To the best of our knowledge, this paper provides the first results on consistency and asymptotic normality of the QML estimator in nonlinear autoregressive models with GARCH errors.

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