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On the statistical estimation of diffusion processes: a survey

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  • Cysne, Rubens Penha

Abstract

Data available on continuos-time diffusions are always sampled discretely in time. In most cases, the likelihood function of the observations is not directly computable. This survey covers a sample of the statistical methods that have been developed to solve this problem. We concentrate on some recent contributions to the literature based on three di§erent approaches to the problem: an improvement of the Euler-Maruyama discretization scheme, the use of Martingale Estimating Functions and the application of Generalized Method of Moments (GMM).

Suggested Citation

  • Cysne, Rubens Penha, 2004. "On the statistical estimation of diffusion processes: a survey," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 540, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
  • Handle: RePEc:fgv:epgewp:540
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    References listed on IDEAS

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    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    3. P. E. Kloeden & Eckhard Platen & H. Schurz & M. Sørensen, 1996. "On effects of discretization on estimators of drift parameters for diffusion processes," Published Paper Series 1996-2, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    4. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    5. Hansen, Lars Peter & Scheinkman, Jose Alexandre, 1995. "Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes," Econometrica, Econometric Society, vol. 63(4), pages 767-804, July.
    6. Yacine Ait-Sahalia, 2002. "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach," Econometrica, Econometric Society, vol. 70(1), pages 223-262, January.
    7. Helle Sørensen, 2002. "Parametric Inference for Diffusion Processes Observed at Discrete Points in Time: a Survey," Discussion Papers 02-08, University of Copenhagen. Department of Economics.
    8. Paul R. Krugman, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(3), pages 669-682.
    9. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

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    5. Fernando de Holanda Barbosa, 2017. "Competitive Equilibrium Hyperinflation Under Rational Expectations," SpringerBriefs in Economics, in: Exploring the Mechanics of Chronic Inflation and Hyperinflation, chapter 0, pages 77-91, Springer.
    6. Horowitz, Andrew W. & Flôres Junior, Renato Galvão, 2004. "Beyond indifferent players: on the existence of prisoners dilemmas in games with amicable and adversarial preferences," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 576, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).

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