Cassim, Lucius (2018): A semiparametric GARCH (1, 1) estimator under serially dependent innovations.

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Abstract
The main objective of this study is to derive semi parametric GARCH (1, 1) estimator under serially dependent innovations. The specific objectives are to show that the derived estimator is not only consistent but also asymptotically normal. Normally, the GARCH (1, 1) estimator is derived through quasimaximum likelihood estimation technique and then consistency and asymptotic normality are proved using the weak law of large numbers and Lindeberg central limit theorem respectively. In this study, we apply the quasimaximum likelihood estimation technique to derive the GARCH (1, 1) estimator under the assumption that the innovations are serially dependent. Allowing serial dependence of the innovations has however brought problems in terms of methodology. Firstly, we cannot split the joint probability distribution into a product of marginal distributions as is normally done. Rather, the study splits the joint distribution into a product of conditional densities to get around this problem. Secondly, we cannot use the weak laws of large numbers or/and the Lindeberg central limit theorem. We therefore employ the martingale techniques to achieve the specific objectives. Having derived the semi parametric GARCH (1, 1) estimator, we have therefore shown that the derived estimator not only converges almost surely to the true population parameter but also converges in distribution to the normal distribution with the highest possible convergence rate similar to that of parametric estimators
Item Type:  MPRA Paper 

Original Title:  A semiparametric GARCH (1, 1) estimator under serially dependent innovations 
English Title:  A semiparametric GARCH (1, 1) estimator under serially dependent innovations 
Language:  English 
Keywords:  GARCH(1,1), semi parametric , Quasi Maximum Likelihood Estimation, Martingale 
Subjects:  C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C58  Financial Econometrics 
Item ID:  86572 
Depositing User:  Mr Lucius Cassim 
Date Deposited:  10 May 2018 04:20 
Last Modified:  10 May 2018 04:20 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/86572 