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Quasi Indirect Inference for Diffusion Processes

Author

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  • BROZE, Laurence

    () (CORE, Universite catholique de Louvain and Universite de Lille 3)

  • SCAILLET, Olivier

    (CREST)

  • ZAKOIAN, Jean-Michel

    (CREST and Université de Lille 1)

Abstract

We present an estimation procedure for continuous time models based on discrete sampled data with a fixed unit of time between two observations. Since in general the conditional likelihood of the model cannot be derived an indirect inference procedure based on simulations of a discretized model is proposed. Asymptotic properties of this quasi indirect estimator are given and some particular cases are examined. Finite sample properties are also considered through Monte Carlo experiments. We also examine the problem of the choice of an appropriate simulation step.

Suggested Citation

  • BROZE, Laurence & SCAILLET, Olivier & ZAKOIAN, Jean-Michel, 1995. "Quasi Indirect Inference for Diffusion Processes," CORE Discussion Papers 1995005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:1995005
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    File URL: https://uclouvain.be/en/research-institutes/immaq/core/dp-1995.html
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    Cited by:

    1. Giorgio Calzolari & Francesca Di Iorio & Gabriele Fiorentini, 2001. "Indirect inference and variance reduction using control variates," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1-2), pages 39-53.
    2. Fiorentini, Gabriele & Leon, Angel & Rubio, Gonzalo, 2002. "Estimation and empirical performance of Heston's stochastic volatility model: the case of a thinly traded market," Journal of Empirical Finance, Elsevier, vol. 9(2), pages 225-255, March.
    3. A. S. Hurn & J. I. Jeisman & K. A. Lindsay, 0. "Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 5(3), pages 390-455.
    4. Giorgio Calzolari & Francesca Di Iorio & Gabriele Fiorentini, 1998. "Control variates for variance reduction in indirect inference: Interest rate models in continuous time," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages 100-112.
    5. Veronika Czellar & Elvezio Ronchetti, 2008. "Accurate and robust indirect inference for diffusion models," Research Papers by the Institute of Economics and Econometrics, Geneva School of Economics and Management, University of Geneva 2008.01, Institut d'Economie et Econométrie, Université de Genève.
    6. Eric Ghysels & Andrew Harvey & Éric Renault, 1995. "Stochastic Volatility," CIRANO Working Papers 95s-49, CIRANO.
    7. Detemple, Jerome & Garcia, Rene & Rindisbacher, Marcel, 2006. "Asymptotic properties of Monte Carlo estimators of diffusion processes," Journal of Econometrics, Elsevier, vol. 134(1), pages 1-68, September.
    8. Stan Hurn & J.Jeisman & K.A. Lindsay, 2006. "Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations. Working paper #2," NCER Working Paper Series 2, National Centre for Econometric Research.
    9. Raknerud, Arvid & Skare, Øivind, 2012. "Indirect inference methods for stochastic volatility models based on non-Gaussian Ornstein–Uhlenbeck processes," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3260-3275.
    10. Kristensen, Dennis, 2008. "Estimation of partial differential equations with applications in finance," Journal of Econometrics, Elsevier, vol. 144(2), pages 392-408, June.
    11. Hafner, Christian M. & Laurent, Sebastien & Violante, Francesco, 2017. "Weak Diffusion Limits Of Dynamic Conditional Correlation Models," Econometric Theory, Cambridge University Press, vol. 33(03), pages 691-716, June.
    12. Di Iorio, Francesca & Calzolari, Giorgio, 2006. "Discontinuities in indirect estimation: An application to EAR models," Computational Statistics & Data Analysis, Elsevier, vol. 50(8), pages 2124-2136, April.
    13. Fornari, Fabio & Mele, Antonio, 2001. "Recovering the probability density function of asset prices using garch as diffusion approximations," Journal of Empirical Finance, Elsevier, vol. 8(1), pages 83-110, March.
    14. Suresh M. Sundaresan, 2000. "Continuous-Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    15. Laurence Broze & Olivier Scaillet & Jean-Michel Zakoïan & Claude Jessua, 1996. "Estimation de modèles de la structure par terme des taux d'intérêt," Revue Économique, Programme National Persée, vol. 47(3), pages 511-519.
    16. Giorgio Calzolari & F. Di Iorio & G. Fiorentini, 1999. "Indirect Estimation of Just-Identified Models with Control Variates," Econometrics Working Papers Archive quaderno46, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    17. Carrasco, Marine & Chernov, Mikhail & Florens, Jean-Pierre & Ghysels, Eric, 2007. "Efficient estimation of general dynamic models with a continuum of moment conditions," Journal of Econometrics, Elsevier, vol. 140(2), pages 529-573, October.
    18. 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.
    19. Fornari, Fabio & Mele, Antonio, 2006. "Approximating volatility diffusions with CEV-ARCH models," Journal of Economic Dynamics and Control, Elsevier, vol. 30(6), pages 931-966, June.
    20. Antonio Mele & Fabio Fornari, 1999. "Stochastic Volatility and the Informational Content of Option Prices: Empirical Analysis," Computing in Economics and Finance 1999 912, Society for Computational Economics.
    21. Dennis Kristensen, 2004. "A Semiparametric Single-Factor Model of the Term Structure," FMG Discussion Papers dp501, Financial Markets Group.
    22. Chiarella, Carl & Hung, Hing & T, Thuy-Duong, 2009. "The volatility structure of the fixed income market under the HJM framework: A nonlinear filtering approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2075-2088, April.
    23. Laurini, Márcio Poletti & Hotta, Luiz Koodi, 2013. "Indirect Inference in fractional short-term interest rate diffusions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 109-126.
    24. Terence D.Agbeyegbe & Elena Goldman, 2005. "Estimation of threshold time series models using efficient jump MCMC," Economics Working Paper Archive at Hunter College 406, Hunter College Department of Economics, revised 2005.
    25. Christensen Bent Jesper & Poulsen Rolf, 2001. "Monte Carlo Improvement of Estimates of the Mean-Reverting Constant Elasticity of Variance Interest Rate Diffusion," Monte Carlo Methods and Applications, De Gruyter, vol. 7(1-2), pages 111-124, December.

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