Geodesic
Use of tempered stable distributions in $GARCH(1, 1)$ models
Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2018), pp. 48-58.

Voir la notice de l'article provenant de la source Math-Net.Ru

Use of classical and modified tempered stable distributions for $GARCH$ models is considered in the paper. 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. Comparison of the properties of stable and tempered stable distributions is presented; methodologies for constructing models and subsequent estimation of parameters using the maximum likelihood method are described. An experimental based on model data comparative analysis of the accuracy of models parameters estimates for different residuals distributions was held, and it confirms the operability of the used methods. An example of building models on real data is considered.
Keywords: $GARCH$ model; stable distribution; tempered stable distribution; maximum likelihood method. 
@article{BGUMI_2018_1_a5,
     author = {U. S. Tserakh},
     title = {Use of tempered stable distributions in $GARCH(1, 1)$ models},
     journal = {Journal of the Belarusian State University. Mathematics and Informatics},
     pages = {48--58},
     publisher = {mathdoc},
     volume = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/BGUMI_2018_1_a5/}
}
TY  - JOUR
AU  - U. S. Tserakh
TI  - Use of tempered stable distributions in $GARCH(1, 1)$ models
JO  - Journal of the Belarusian State University. Mathematics and Informatics
PY  - 2018
SP  - 48
EP  - 58
VL  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BGUMI_2018_1_a5/
LA  - ru
ID  - BGUMI_2018_1_a5
ER  - 
%0 Journal Article
%A U. S. Tserakh
%T Use of tempered stable distributions in $GARCH(1, 1)$ models
%J Journal of the Belarusian State University. Mathematics and Informatics
%D 2018
%P 48-58
%V 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BGUMI_2018_1_a5/
%G ru
%F BGUMI_2018_1_a5
U. S. Tserakh. Use of tempered stable distributions in $GARCH(1, 1)$ models. Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2018), pp. 48-58. http://geodesic.mathdoc.fr/item/BGUMI_2018_1_a5/

[1] T. Bollerslev, “Generalized autoregressive conditional heteroscedasticity”, J. econom, 31(3) (1986), 307–327 | DOI | MR | Zbl

[2] M. S. Paolella, “Stable-GARCH models for financial returns: Fast estimation and tests for stability”, Econometrics, 4(2) (2016), 1–28 | DOI

[3] C. Francq, S. G. Meintanis, “Fourier-type estimation of the power GARCH model with stable-paretian innovations”, Metrika, 79 (2016), 389–424 | DOI | MR | Zbl

[4] V. S. Terekh, N. N. Trush, “Issledovanie modelei GARCH(1, 1) s ustoichivymi vozmuscheniyami”, XII Belorusskaya matematicheskaya konferentsiya (Minsk), 2016, 14

[5] I. Koponen, “Analytic approach to the problem of convergence of truncated Levy flights towards the Gaussian stochastic process”, Phys. Rev. E, 52 (1995), 1197–1199 | DOI

[6] Y. S. Kim, S. T. Rachev, D. M. Chung, “The modified tempered stable distribution, GARCH-models and option pricing”, Technical report, Chair of Econometrics, Statistics and Mathematical Finance School of Economics and Business Engineering University of Karlsruhe, 2006

[7] V. S. Terekh, “Postroenie i issledovanie svoistv M-otsenki parametrov modeli GARCH(1, 1)”, Sbornik rabot 72-i nauchnoi konferentsii studentov i aspirantov Belorusskogo gosudarstvennogo universiteta (Minsk), 2015, 112–115