Parrini, Alessandro (2012): Indirect estimation of GARCH models with alphastable innovations.

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Abstract
Several studies have highlighted the fact that heavytailedness of asset returns can be the consequence of conditional heteroskedasticity. GARCH models have thus become very popular, given their ability to account for volatility clustering and, implicitly, heavy tails. However, these models encounter some difficulties in handling financial time series, as they respond equally to positive and negative shocks and their tail behavior remains too short even with Studentt error terms. To overcome these weaknesses we apply GARCHtype models with alphastable innovations. The stable family of distributions constitutes a generalization of the Gaussian distribution that has intriguing theoretical and practical properties. Indeed it is stable under addiction and, having four parameters, it allows for asymmetry and heavy tails. Unfortunately stable models do not have closed likelihood function, but since simulated values from αstable distributions can be straightforwardly obtained, the indirect inference approach is particularly suited to the situation at hand. In this work we provide a description of how to estimate a GARCH(1,1) and a TGARCH(1,1) with symmetric stable shocks using as auxiliary model a GARCH(1,1) with skewt innovations. Monte Carlo simulations, conducted using GAUSS, are presented and finally the proposed models are used to estimate the IBM weekly return series as an illustration of how they perform on real data.
Item Type:  MPRA Paper 

Original Title:  Indirect estimation of GARCH models with alphastable innovations 
Language:  English 
Keywords:  GARCH, alphastable distribution, indirect estimation, skewt distribution, Monte Carlo simulations 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C32  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models C  Mathematical and Quantitative Methods > C8  Data Collection and Data Estimation Methodology ; Computer Programs > C87  Econometric Software C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C15  Statistical Simulation Methods: General C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics 
Item ID:  38544 
Depositing User:  Alessandro Parrini 
Date Deposited:  04. May 2012 13:11 
Last Modified:  27. Apr 2015 17:55 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/38544 