Indirect estimation of GARCH models with alpha-stable innovations

Alessandro Parrini ()

MPRA Paper from University Library of Munich, Germany

Abstract: Several studies have highlighted the fact that heavy-tailedness 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 Student-t error terms. To overcome these weaknesses we apply GARCH-type models with alpha-stable 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 α-stable 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 skew-t 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.

Keywords: GARCH; alpha-stable distribution; indirect estimation; skew-t distribution; Monte Carlo simulations (search for similar items in EconPapers)
JEL-codes: C01 C13 C15 C32 C87 (search for similar items in EconPapers)
Date: 2012-04-18
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://mpra.ub.uni-muenchen.de/38544/1/MPRA_paper_38544.pdf original version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:38544

Access Statistics for this paper

More papers in MPRA Paper from University Library of Munich, Germany Ludwigstraße 33, D-80539 Munich, Germany. Contact information at EDIRC.
Bibliographic data for series maintained by Joachim Winter ().