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The Pearson diffusions: A class of statistically tractable diffusion processes

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  • Michael Sørensen
  • Julie Lyng Forman

    ()
    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

Abstract

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.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2007-28.

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Length: 32
Date of creation: 27 Sep 2007
Date of revision:
Handle: RePEc:aah:create:2007-28

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Web page: http://www.econ.au.dk/afn/

Related research

Keywords: eigenfunction; ergodic diffusion; integrated diffusion; martingale estimating function; likelihood inference; mixing; optimal estimating function; Pearson system; prediction based estimating function; quasi likelihood; spectral methods; stochastic differential equation; stochastic volatility;

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  1. Meddahi, N., 2001. "A Theoretical Comparison Between Integrated and Realized Volatilies," Cahiers de recherche 2001-26, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  7. 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.).
  8. Chacko, George & Viceira, Luis M., 2003. "Spectral GMM estimation of continuous-time processes," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 259-292.
  9. Gourieroux, Christian & Jasiak, Joann, 2006. "Multivariate Jacobi process with application to smooth transitions," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 475-505.
  10. 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.
  11. 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.
  12. Bent Jesper Christensen & Michael Sørensen, 2008. "Optimal inference in dynamic models with conditional moment restrictions," CREATES Research Papers 2008-51, School of Economics and Management, University of Aarhus.
  13. 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.
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Cited by:
  1. Almut E. D. Veraart & Luitgard A. M. Veraart, 2009. "Stochastic volatility and stochastic leverage," CREATES Research Papers 2009-20, School of Economics and Management, University of Aarhus.
  2. Aleksandar Mijatovic & Paul Schneider, 2009. "Empirical asset pricing with nonlinear risk premia," Papers 0911.0928, arXiv.org.
  3. Yuichi Nagahara, 2011. "Using Nonnormal Distributions to Analyze the Relationship Between Stock Returns in Japan and the US," Asia-Pacific Financial Markets, Springer, vol. 18(4), pages 429-443, November.
  4. Asger Lunde & Anne Floor Brix, 2013. "Estimating Stochastic Volatility Models using Prediction-based Estimating Functions," CREATES Research Papers 2013-23, School of Economics and Management, University of Aarhus.
  5. Christa Cuchiero & Martin Keller-Ressel & Josef Teichmann, 2012. "Polynomial processes and their applications to mathematical finance," Finance and Stochastics, Springer, vol. 16(4), pages 711-740, October.
  6. Filipović, Damir & Mayerhofer, Eberhard & Schneider, Paul, 2013. "Density approximations for multivariate affine jump-diffusion processes," Journal of Econometrics, Elsevier, vol. 176(2), pages 93-111.
  7. Yuichi Nagahara, 2008. "A Method of Calculating the Downside Risk by Multivariate Nonnormal Distributions," Asia-Pacific Financial Markets, Springer, vol. 15(3), pages 175-184, December.

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