Dependence structure of stable R-GARCH processes

• Autorzy: Nowicka-Zagrajek J. , Weron A.
• Języki publikacji: EN

Abstrakty

EN

In this paper we investigate properties of R-GARCH processes with positive strictly stable innovations. We derive the unconditional distributions and analyze the dependence structure. This analysis is carried out by means of the measure of dependence - the codifference - which extends the behavior of the covariance function to situations where the covariance function is no longer defined. In the case of R-GARCH (1,1,0) process we determine the exact asymptotic behavior.

Słowa kluczowe

EN

GARCH process; covariance function; dependence structure

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2001
• Tom: Vol. 21, Fasc. 2
• Strony: 371--380
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Nowicka-Zagrajek J.

• Hugo Steinhaus Center, Institute of Mathematics, Wroclaw University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wroclaw

autor

Weron A.

• Hugo Steinhaus Center, Institute of Mathematics, Wroclaw University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wroclaw

Bibliografia

• [1] T. Boilers!ev, R. Y. Chou and K. F. Kroner, RCT modeling in finance, 1 Econometrics 52 (1992), pp. 5-59.
• [2] C. Gourieroux, ARCH Models and Financial Applications, Springer, New York 1997.
• [3] U. A. Müller, M. M. Dacorogna, R. Davé, R. B. Olsen, O. V. Pictet and J. E. von Weizsäcker, Volatilities of Different Time Resolutions - Analysing the Dynamics of Market Components, Journal of Empirical Finance 4 (2 -3) (1997), pp, 213-240.
• [4] J. Nowicka, Analysys of measures of dependence for time series with α-stable innovations, Ph.D. Thesis, Wroclaw University of Technology, 1998.
• [5] A. K. Panorska, S. Mittnik and S. T. Rachev, Stable GJARCH Models for Financial Time Series, Appl. Math. Lett 8 (5) (1995), pp. 33-37.
• [6] G. Samorodnitsky and M. S, Taqqu, Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance, Chapman & Hall, New York 1994.
• [7] C de Vries, On the relation between GARCH and stable processes, J. Econometrics 48 (199.1), pp. 313-324.
• [8] A. Weron and R. Weron, Financial Engineering: Derivatives Pricing, Computer Simulations, Market Statistics (in Polish), WNT, Warszawa 1998.
• [9] R. Weron, Lévy-stable distributions revisited: tail index 2 does not exclude the Lévy-stable regime, International Journal of Modern Physics C 12 (2001), pp. 209-223.