# Parameter Estimation for Non-Stationary Fisher-Snedecor Diffusion

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## 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

## Mathematics Subject Classification (2010)

33C05 33C47 35P10 60G10 60J60 62M05 62M15## Preview

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## Notes

### Acknowledgments

N.N. Leonenko was supported in particular by Cardiff Incoming Visiting Fellowship Scheme and International Collaboration Seedcorn Fund, Cardiff Data Innovation Research Institute Seed Corn Funding, Australian Research Council’s Discovery Projects funding scheme (project number DP160101366), and by projects MTM2012-32674 and MTM2015-71839-P (co-funded with Federal funds), of the DGI, MINECO, Spain.

N. Šuvak and I. Papić were supported by the scientific project UNIOS-ZUP 2018-31 funded by the J. J. Strossmayer University of Osijek.

At last, authors would like to thank Danijel Grahovac (Department of Mathematics, J.J. Strossmayer University of Osijek) for many useful discussions regarding the tail-index estimation.

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