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Computational Aspects Related to Martingale Estimating Functions for a Discretely Observed Diffusion

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  • MATHIEU KESSLER
  • SILVESTRE PAREDES

Abstract

Martingale estimating functions for a discretely observed diffusion have turned out to provide estimators with nice asymptotic properties. However, their expression usually involves some conditional expectation that has to be evaluated through Monte Carlo simulations giving rise to an approximated estimator. In this work we study, for ergodic models, the asymptotic properties of the approximated estimator and describe the influence of the number of independent simulated trajectories involved in the Monte Carlo method as well as of the approximation scheme used. Our results are of practical relevance to assess the implementation of martingale estimating functions for discretely observed diffusions.

Suggested Citation

  • Mathieu Kessler & Silvestre Paredes, 2002. "Computational Aspects Related to Martingale Estimating Functions for a Discretely Observed Diffusion," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 425-440, September.
    • Handle: RePEc:bla:scjsta:v:29:y:2002:i:3:p:425-440
    DOI: 10.1111/1467-9469.00299
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    Citations

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    Cited by:

    1. Friedrich Hubalek & Petra Posedel, 2008. "Asymptotic analysis for a simple explicit estimator in Barndorff-Nielsen and Shephard stochastic volatility models," Papers 0807.3479, arXiv.org.
    2. 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.
    3. Leah Kelly, 2004. "Inference and Intraday Analysis of Diversified World Stock Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 24, July-Dece.
    4. Zhang, Shulin & Song, Peter X.-K. & Shi, Daimin & Zhou, Qian M., 2012. "Information ratio test for model misspecification on parametric structures in stochastic diffusion models," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3975-3987.
    5. Mathieu Kessler & Michael Sørensen, 2005. "On Time-Reversibility and Estimating Functions for Markov Processes," Statistical Inference for Stochastic Processes, Springer, vol. 8(1), pages 95-107, January.
    6. J. Jimenez & R. Biscay & T. Ozaki, 2005. "Inference Methods for Discretely Observed Continuous-Time Stochastic Volatility Models: A Commented Overview," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 12(2), pages 109-141, June.
    7. Leah Kelly, 2004. "Inference and Intraday Analysis of Diversified World Stock Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2004.
    8. Friedrich Hubalek & Petra Posedel, 2011. "Joint analysis and estimation of stock prices and trading volume in Barndorff-Nielsen and Shephard stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 11(6), pages 917-932.
    9. Michael Sørensen, 2008. "Parametric inference for discretely sampled stochastic differential equations," CREATES Research Papers 2008-18, Department of Economics and Business Economics, Aarhus University.
    10. A. M. Kulik & N. N. Leonenko & I. Papić & N. Šuvak, 2020. "Parameter Estimation for Non-Stationary Fisher-Snedecor Diffusion," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1023-1061, September.

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