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.

中文翻译：

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非平稳Fisher-Snedecor扩散的参数估计

考虑具有Fisher-Snedecor不变分布的非平稳遍历扩散的参数估计问题，称为Fisher-Snedecor扩散。基于连续时间观测，我们提出了未知参数的广义矩估计器，并证明了其一致性和渐近正态性。渐近正态性框架中的渐近协方差矩阵的显式形式是根据基于点协变的演化方程的新迭代技术计算出来的。在涵盖各种起始分布和参数值的仿真研究中说明了结果。