@article{8cb41881e494497fba50c7f4db41893f,
title = "Stable GARCH models for financial time series",
abstract = "Generalized autoregressive conditional heteroskedasticity (GARCH) models having normal or Student-t distributions as conditional distributions are widely used in financial modeling. Normal or Student-t distributions may be inappropriate for very heavy-tailed times series as can be encountered in financial economics, for example. Here, we propose GARCH models with stable Paretian conditional distributions to deal with such time series. We state conditions for stationarity and discuss simulation aspects.",
keywords = "ARCH, Fat-tailed distributions, Financial modelling, GARCH, Stable distributions",
author = "Panorska, {A. K.} and S. Mittnik and Rachev, {S. T.}",
note = "Funding Information: The class of autoregressive conditional heteroskedasticity (ARCH) models was introduced in \[1\], to allow the conditional variance of a time series process to depend on past information. A generalization to so-called generalized ARCH (GARCH) processes was proposed in \[2\].A RCH and GARCH models are now widely used to model financial time series \[3\].T his paper introduces GARCH processes whose conditional distribution are stable Paretian or, in short, stable GARCH processes. We provide necessary and sufficient conditions for the existence and uniquness of stationary solutions and address the simulation of stationary stable GARCH processes. An important assumption of GARCH models is that the conditional distribution of the process possesses second moments, imposing limits on the heaviness of the tails of its unconditional distribution. Given that a wide range of financial data exhibit remarkably fat tails, this assumption represents a major shortcoming of GARCH models in financial time series analysis. This observation has led to the use of the Student t instead of normal distribution as the conditional distribution (see for example \[4,5\]). The Student t distribution allows for heavier tails than the normal distribution, but--in contrast to the normal distribution--lacks the desirable stability property. Stability is desirable, because stable distributions have domains of attraction, and The research of this author was partially supported by a CECA Scholars Grant and a UTC Faculty Research Grant.",
year = "1995",
month = sep,
doi = "10.1016/0893-9659(95)00063-V",
language = "English",
volume = "8",
pages = "33--37",
journal = "Applied Mathematics Letters",
issn = "0893-9659",
number = "5",
}