The Pearson diffusions: A class of statistically tractable diffusion processes
The Pearson diffusions is a flexible class of diffusions defined by having linear drift and quadratic squared diffusion coefficient. It is demonstrated that for this class explicit statistical inference is feasible. Explicit optimal martingale estimating func- tions are found, and the corresponding estimators are shown to be consistent and asymptotically normal. The discussion covers GMM, quasi-likelihood, and non- linear weighted least squares estimation too, and it is discussed how explicit likeli- hood or approximate likelihood inference is possible for the Pearson diffusions. A complete model classification is presented for the ergodic Pearson diffusions. The class of stationary distributions equals the full Pearson system of distributions. Well-known instances are the Ornstein-Uhlenbeck processes and the square root (CIR) processes. Also diffusions with heavy-tailed and skew marginals are included. Special attention is given to a skew t-type distribution. Explicit formulae for the conditional moments and the polynomial eigenfunctions are derived. The analyti- cal tractability is inherited by transformed Pearson diffusions, integrated Pearson diffusions, sums of Pearson diffusions, and stochastic volatility models with Pearson volatility process. For the non-Markov models explicit optimal prediction based estimating functions are found and shown to yield consistent and asymptotically normal estimators.
|Date of creation:||27 Sep 2007|
|Date of revision:|
|Contact details of provider:|| Web page: http://www.econ.au.dk/afn/|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Eric Ghysels & Jean-Pierre Florens & Mikhail Chernov & Marine Carrasco, 2003.
"Efficient Estimation of Jump Diffusions and General Dynamic Models with a Continuum of Moment Conditions,"
CIRANO Working Papers
- Carrasco, Marine & Chernov, Mikhaël & Florens, Jean-Pierre & Ghysels, Eric, 2000. "Efficient Estimation of Jump Diffusions and General Dynamic Models with a Continuum of Moment Conditions," IDEI Working Papers 116, Institut d'Économie Industrielle (IDEI), Toulouse, revised 2002.
- Hao Zhou, 2003.
"Itô conditional moment generator and the estimation of short rate processes,"
Finance and Economics Discussion Series
2003-32, Board of Governors of the Federal Reserve System (U.S.).
- Hao Zhou, 2003. "Itô Conditional Moment Generator and the Estimation of Short-Rate Processes," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(2), pages 250-271.
- MEDDAHI, Nour, 2001.
"A Theoretical Comparison Between Integrated and Realized Volatilies,"
Cahiers de recherche
2001-26, Universite de Montreal, Departement de sciences economiques.
- Nour Meddahi, 2002. "A theoretical comparison between integrated and realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 479-508.
- Meddahi, N., 2001. "A Theoretical Comparison Between Integrated and Realized Volatilies," Cahiers de recherche 2001-26, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Bent Jesper Christensen & Michael Sørensen, 2008. "Optimal inference in dynamic models with conditional moment restrictions," CREATES Research Papers 2008-51, Department of Economics and Business Economics, Aarhus University.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- Gourieroux, Christian & Jasiak, Joann, 2006. "Multivariate Jacobi process with application to smooth transitions," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 475-505.
- Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
- Hansen, Lars Peter & Alexandre Scheinkman, Jose & Touzi, Nizar, 1998. "Spectral methods for identifying scalar diffusions," Journal of Econometrics, Elsevier, vol. 86(1), pages 1-32, June.
- Tim Bollerslev & Hao Zhou, 2001.
"Estimating stochastic volatility diffusion using conditional moments of integrated volatility,"
Finance and Economics Discussion Series
2001-49, Board of Governors of the Federal Reserve System (U.S.).
- Bollerslev, Tim & Zhou, Hao, 2002. "Estimating stochastic volatility diffusion using conditional moments of integrated volatility," Journal of Econometrics, Elsevier, vol. 109(1), pages 33-65, July.
- Susanne Ditlevsen & Michael Sørensen, 2004. "Inference for Observations of Integrated Diffusion Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(3), pages 417-429.
- Chacko, George & Viceira, Luis M., 2003. "Spectral GMM estimation of continuous-time processes," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 259-292.
- Arnaud Gloter, 2006. "Parameter Estimation for a Discretely Observed Integrated Diffusion Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(1), pages 83-104.
- Singleton, Kenneth J., 2001. "Estimation of affine asset pricing models using the empirical characteristic function," Journal of Econometrics, Elsevier, vol. 102(1), pages 111-141, May.
When requesting a correction, please mention this item's handle: RePEc:aah:create:2007-28. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.