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Parameter Estimation for Non-Stationary Fisher-Snedecor Diffusion

Author

Listed:
  • A. M. Kulik

    (Wroclaw University of Science and Technology)

  • N. N. Leonenko

    (Cardiff University)

  • I. Papić

    (J.J. Strossmayer University of Osijek)

  • N. Šuvak

    (J.J. Strossmayer University of Osijek)

Abstract

The problem of parameter estimation for the non-stationary ergodic diffusion with Fisher-Snedecor invariant distribution, to be called Fisher-Snedecor diffusion, is considered. We propose generalized method of moments (GMM) estimator of unknown parameter, based on continuous-time observations, and prove its consistency and asymptotic normality. The explicit form of the asymptotic covariance matrix in asymptotic normality framework is calculated according to the new iterative technique based on evolutionary equations for the point-wise covariations. The results are illustrated in a simulation study covering various starting distributions and parameter values.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:3:d:10.1007_s11009-019-09755-z
    DOI: 10.1007/s11009-019-09755-z
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    References listed on IDEAS

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    1. Julie Lyng Forman & Michael Sørensen, 2008. "The Pearson Diffusions: A Class of Statistically Tractable Diffusion Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 438-465, September.
    2. Mathieu Kessler, 2000. "Simple and Explicit Estimating Functions for a Discretely Observed Diffusion Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(1), pages 65-82, March.
    3. 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.
    4. Kulik, Alexey M., 2011. "Asymptotic and spectral properties of exponentially [phi]-ergodic Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 121(5), pages 1044-1075, May.
    5. William Shaw & Asad Munir, 2009. "Dependency without copulas or ellipticity," The European Journal of Finance, Taylor & Francis Journals, vol. 15(7-8), pages 661-674.
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