Fourier--type estimation of the power garch model with stable--paretian innovations
We consider estimation for general power GARCH models under stable--Paretian innovations. Exploiting the simple structure of the conditional characteristic function of the observations driven by these models we propose minimum distance estimation based on the empirical characteristic function of corresponding residuals. Consistency of the estimators is proved, and we obtain a singular asymptotic distribution which is concentrated on a hyperplane. Efficiency issues are explored and finite--sample results are presented as well as applications of the proposed procedures to real data from the financial markets. A multivariate extension is also considered.
|Date of creation:||01 Oct 2012|
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- John L. Knight & Stephen E. Satchell & Jun Yu, 2002. "Estimation of the Stochastic Volatility Model by the Empirical Characteristic Function Method," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 44(3), pages 319-335, 09.
- Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
- Liu, Shi-Miin & Brorsen, B Wade, 1995. "Maximum Likelihood Estimation of a Garch-Stable Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(3), pages 273-285, July-Sept.
- Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
- Mittnik, Stefan & Paolella, Marc S. & Rachev, Svetlozar T., 2002. "Stationarity of stable power-GARCH processes," Journal of Econometrics, Elsevier, vol. 106(1), pages 97-107, January.
- Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
- Kotchoni, Rachidi, 2012.
"Applications of the characteristic function-based continuum GMM in finance,"
Computational Statistics & Data Analysis,
Elsevier, vol. 56(11), pages 3599-3622.
- Rachidi Kotchoni, 2012. "Applications of the Characteristic Function Based Continuum GMM in Finance," Post-Print hal-00867795, HAL.
- Matteo Bonato, 2012. "Modeling fat tails in stock returns: a multivariate stable-GARCH approach," Computational Statistics, Springer, vol. 27(3), pages 499-521, September.
- Carrasco, Marine & Chernov, Mikhail & Florens, Jean-Pierre & Ghysels, Eric, 2007. "Efficient estimation of general dynamic models with a continuum of moment conditions," Journal of Econometrics, Elsevier, vol. 140(2), pages 529-573, October.
- Sucharita Ghosh & Jan Beran, 2006. "On Estimating the Cumulant Generating Function of Linear Processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(1), pages 53-71, March.
- Davis, Richard A. & Knight, Keith & Liu, Jian, 1992. "M-estimation for autoregressions with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 145-180, February.
- Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
- Jun Yu, 2004. "Empirical Characteristic Function Estimation and Its Applications," Econometric Reviews, Taylor & Francis Journals, vol. 23(2), pages 93-123.
- Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394-394.
- Emanuele Taufer, 2008. "Characteristic function estimation of non-Gaussian Ornstein-Uhlenbeck processes," DISA Working Papers 0805, Department of Computer and Management Sciences, University of Trento, Italy, revised 07 Jul 2008.
- Liu, Shi-Miin & Brorsen, B Wade, 1995. "GARCH-Stable as a Model of Futures Price Movements," Review of Quantitative Finance and Accounting, Springer, vol. 5(2), pages 155-167, June.
- Davis, Richard A., 1996. "Gauss-Newton and M-estimation for ARMA processes with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 63(1), pages 75-95, October. Full references (including those not matched with items on IDEAS)
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