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Uniform Ergodicity of an Exponential Continuous Time GARCH(p,q) Model
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 Title & Authors
Uniform Ergodicity of an Exponential Continuous Time GARCH(p,q) Model
Lee, Oe-Sook;
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 Abstract
The exponential continuous time GARCH(p,q) model for financial assets suggested by Haug and Czado (2007) is considered, where the log volatility process is driven by a general Lvy process and the price process is then obtained by using the same Lvy process as driving noise. Uniform ergodicity and -mixing property of the log volatility process is obtained by adopting an extended generator and drift condition.
 Keywords
Exponential continuous time GARCH(p,q) model;stationarity;uniform ergodicity;-mixing;-mixing;
 Language
English
 Cited by
 References
1.
Applebaum, D. (2004). Levy Processes and Stochastic Calculus, Cambridge University Press.

2.
Bradley, R. (2005). Basic properties of strong mixing conditions: A survey and some open questions, Probability Surveys, 2, 107-144. crossref(new window)

3.
Brockwell, P. J. (2001). Levy driven CARMA process, Annals of the Institute of Statistical Mathematics, 53, 113-124. crossref(new window)

4.
Brockwell, P., Chadraa, E. and Lindner, A. (2006). Continuous time GARCH processes, Annals of Applied Probability, 16, 790-826. crossref(new window)

5.
Bockwell, P. and Marquardt, T. (2005). Levy driven and Fractionally integrated ARMA processes with continuous time parameter, Statistica Sinica, 15, 477-494.

6.
Doukhan, P. (1994). Mixing: Properties and Examples, Lecture Note in Statistics 85, Springer-Verlag, New York.

7.
Down, D., Meyn, S. P. and Tweedie, R. L. (1995). Exponential and uniform ergodicity of Markov processes, The Annals of Probability, 23, 1671-1691. crossref(new window)

8.
Haug, S. and Czado, C. (2007). An exponential continuous time GARCH process, Journal of Applied Probability, 44, 960-976. crossref(new window)

9.
Lindner, A. (2007). Continuous time GARCH processes, Handbook of Financial Mathematics, Springer-Verlag.

10.
Masuda, H. (2004). On multidimensional Ornstein-Uhlenbeck processes driven by a general Levy process, Bernoulli, 10, 97-120. crossref(new window)

11.
Masuda, H. (2007). Ergodicity and exponential $\beta$-mixing bounds for multidimensional diffusions with jumps, Stochastic Processes and Their Applications, 117, 35-56. crossref(new window)

12.
Meyn, S. P. and Tweedie, R. L. (1993a). Markov Chains and Stochastic Stability, Springer-Verlag, Berlin.

13.
Meyn, S. P. and Tweedie, R. L. (1993b). Stability of Markovian processes III: Foster-Lyapunov criteria for continuous time processes, Advances in Applied Probability, 25, 518-548. crossref(new window)

14.
Nelson, D. B. (1991). Conditional heteroscedasticity in asset returns: A new approach, Econometrica, 59, 347-370. crossref(new window)

15.
Protter, P. E. (2005). Stochastic Integration and Differential Equations, 2nd Ed., Springer.

16.
Sato, K. (1999). Levy Processes and Infinitely Divisible Distributions, Cambridge University press, Cambridge.