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GARCH(1,1) models with stable residuals

Trusz M., Tserakh U.

Studia Informatica : systems and information technology

2018

Vol. 1-2(22)

47--57

The focus of this paper is the use of stable distributions for GARCH models. Such models are applied for the analysis of financial and economic time series, which have several special properties: volatility clustering, heavy tails and asymmetry of residuals distributions. Below we compare the properties of stable and tempered stable distributions and describe methodologies for constructing models and subsequent estimation of parameters using the maximum likelihood method. We also analyze an example of building models on real data in order to illustrate that tempered stable distributions could be used in financial time series models. Moreover, such distributions can show better results in comparison with traditionally used distributions.

Pierwsze dwa momenty oceny wariogramu

Trusz M., Arcimowicz I.

Studia Informatica : systems and information technology

2005

Vol. 1(5)

27--33

In this article we deal with theoretical bases of geostatistic which have employment in research of time series. Let we have stationary random process, defined on R, with expected value equal 0, given covariance function and spectral density. For this process we define variogram function and prove two theorems about variogram estimator property.