Preminger, Arie and Storti, Giuseppe (2014): Least squares estimation for GARCH (1,1) model with heavy tailed errors.

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Abstract
GARCH (1,1) models are widely used for modelling processes with time varying volatility. These include financial time series, which can be particularly heavy tailed. In this paper, we propose a logtransformbased least squares estimator (LSE) for the GARCH (1,1) model. The asymptotic properties of the LSE are studied under very mild moment conditions for the errors. We establish the consistency, asymptotic normality at the standard convergence rate of square rootofn for our estimator. The finite sample properties are assessed by means of an extensive simulation study. Our results show that LSE is more accurate than the quasimaximum likelihood estimator (QMLE) for heavy tailed errors. Finally, we provide some empirical evidence on two financial time series considering daily and high frequency returns. The results of the empirical analysis suggest that in some settings, depending on the specific measure of volatility adopted, the LSE can allow for more accurate predictions of volatility than the usual Gaussian QMLE.
Item Type:  MPRA Paper 

Original Title:  Least squares estimation for GARCH (1,1) model with heavy tailed errors 
English Title:  Least squares estimation for GARCH (1,1) model with heavy tailed errors 
Language:  English 
Keywords:  GARCH (1,1), least squares estimation, consistency, asymptotic normality. 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C15  Statistical Simulation Methods: General C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes 
Item ID:  59082 
Depositing User:  Prof. Giuseppe Storti 
Date Deposited:  04 Oct 2014 21:54 
Last Modified:  26 Sep 2019 15:37 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/59082 