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Characteristic function estimation of non-Gaussian Ornstein-Uhlenbeck processes

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Author Info
Emanuele Taufer () (DISA, Faculty of Economics, Trento University)

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Abstract

Continuous non-Gaussian stationary processes of the OU-type are becoming increasingly popular given their flexibility in modelling stylized features of financial series such as asymmetry, heavy tails and jumps. The use of non-Gaussian marginal distributions makes likelihood analysis of these processes unfeasible for virtually all cases of interest. This paper exploits the self-decomposability of the marginal laws of OU processes to provide explicit expressions of the characteristic function which can be applied to several models as well as to develop e±cient estimation techniques based on the empirical characteristic function. Extensions to OU-based stochastic volatility models are provided.

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Paper provided by Department of Computer and Management Sciences, University of Trento, Italy in its series DISA Working Papers with number 0805.

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Length: 20 pages
Date of creation: Jul 2008
Date of revision: 07 Jul 2008
Handle: RePEc:trt:disawp:0805

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Related research
Keywords: Ornstein-Uhlenbeck process; Lévy process; self-decomposable distribution; characteristic function; estimation;

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  1. Jiang, George J & Knight, John L, 2002. "Estimation of Continuous-Time Processes via the Empirical Characteristic Function," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 198-212, April.
  2. Knight, John L. & Satchell, Stephen E., 1997. "The Cumulant Generating Function Estimation Method," Econometric Theory, Cambridge University Press, vol. 13(02), pages 170-184, April. [Downloadable!]
  3. Woerner, Jeannette H.C., 2004. "Estimating The Skewness In Discretely Observed L Vy Processes," Econometric Theory, Cambridge University Press, vol. 20(05), pages 927-942, October. [Downloadable!]
  4. 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. [Downloadable!] (restricted)
  5. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal Of The Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241. [Downloadable!] (restricted)
  6. Ole E. Barndorff-Nielsen, 2003. "Integrated OU Processes and Non-Gaussian OU-based Stochastic Volatility Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association and Swedish Statistical Association, vol. 30(2), pages 277-295. [Downloadable!] (restricted)
  7. Pap, Gyula & van Zuijlen, Martien C. A., 1996. "Parameter Estimation with Exact Distribution for Multidimensional Ornstein-Uhlenbeck Processes," Journal of Multivariate Analysis, Elsevier, vol. 59(2), pages 153-165, November. [Downloadable!] (restricted)
  8. Knight, John L. & Yu, Jun, 2002. "Empirical Characteristic Function In Time Series Estimation," Econometric Theory, Cambridge University Press, vol. 18(03), pages 691-721, June. [Downloadable!]
  9. Ole E. Barndorff-Nielsen & Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal Of The Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280. [Downloadable!] (restricted)
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  10. Geurt Jongbloed & Frank H. Van Der Meulen, 2006. "Parametric Estimation for Subordinators and Induced OU Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association and Swedish Statistical Association, vol. 33(4), pages 825-847. [Downloadable!] (restricted)
  11. Sucharita Ghosh & Jan Beran, 2006. "On Estimating the Cumulant Generating Function of Linear Processes," Annals of the Institute of Statistical Mathematics, Springer, vol. 58(1), pages 53-71, March. [Downloadable!] (restricted)
  12. Taufer, Emanuele & Leonenko, Nikolai, 2009. "Simulation of Lvy-driven Ornstein-Uhlenbeck processes with given marginal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2427-2437, April. [Downloadable!] (restricted)
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  13. Gareth O. Roberts & Omiros Papaspiliopoulos & Petros Dellaportas, 2004. "Bayesian inference for non-Gaussian Ornstein-Uhlenbeck stochastic volatility processes," Journal Of The Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 369-393. [Downloadable!] (restricted)
  14. Griffin, J.E. & Steel, M.F.J., 2006. "Inference with non-Gaussian Ornstein-Uhlenbeck processes for stochastic volatility," Journal of Econometrics, Elsevier, vol. 134(2), pages 605-644, October. [Downloadable!] (restricted)
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