GARCH(1,1) models with stable residuals

• Autorzy: Trusz M. , Tserakh U.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

GARCH model; stable distributions; tempered stable distribution; maximum likelihood method

• Wydawca: Wydawnictwo Uniwersytetu Przyrodniczo-Humanistycznego w Siedlcach
• Czasopismo: Studia Informatica : systems and information technology
• Rocznik: 2018
• Tom: Vol. 1-2(22)
• Strony: 47--57
• Opis fizyczny: Bibliogr. 8 poz., tab.

Twórcy

autor

Trusz M.

• Siedlce University of Natural Sciences and Humanities, Institute of Computer Science, ul. 3 Maja 54, 08-110 Siedlce, Poland

autor

Tserakh U.

• Belarusian State University, Nezavisimosty pr., 4 Minsk, Republic of Belarus

Bibliografia

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• 2. Paolella Marc S., (2016), Stable-GARCH Models for Financial Returns: Fast Estimation and Tests for Stability, Econometrics, 4, issue 2, p. 1-28.
• 3. Francq Christian, G. Meintanis Simos. (2016). Fourier-type estimation of the power GARCH model with stable-Paretian innovations. Metrika, 79, p. 389-424.
• 4. Tserakh U. S., Troush N. N. (2016) GARCH(1,1) models with stable perturbations. The 12th Belarusian Mathematical Conference (abstracts), Minsk, p. 14.
• 5. Koponen I. (1995). Analytic approach to the problem of convergence of truncated Lévy flights towards the Gaussian stochastic process, Physical Review E, 52, p.1197-1199.
• 6. Kim Y. S., Rachev S., Chung D., Bianchi M. (2009). The modified tempered stable distribution, GARCH-models and option pricing. Probability and Mathematical Statistics, 29, isuue 1, p. 91-117.
• 7. Kim Y. S., Rachev S., Bianchi M., Fabozzi F. J. (2008). A new tempered stable distribution and its application to finance. Risk Assessment: Decisions in Banking and Finance, p. 51-84.
• 8. Tserakh U. S. (2015) M-estimate of GARCH(1,1) model parameters computation and exploration. The 72nd Scientific BSU Conference (abstracts), Minsk, issue 1, p. 112-115.