Parameter Estimation for Non-Stationary Fisher-Snedecor Diffusion

A. M. Kulik (), N. N. Leonenko (), I. Papić () and N. Šuvak ()
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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

Methodology and Computing in Applied Probability, 2020, vol. 22, issue 3, 1023-1061

Abstract: 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.

Keywords: Fisher-Snedecor diffusion; Generalized method of moments (GMM); P-consistency; Asymptotic normality; Iterative technique for the calculation of the asymptotic covariance matrix; 33C05; 33C47; 35P10; 60G10; 60J60; 62M05; 62M15 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s11009-019-09755-z

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