Hypothesis testing for Fisher-Snedecor diffusion

We consider the problem of testing the hypothesis on marginal distribution of ergodic diffusion with Fisher-Snedecor invariant distribution, to be called Fisher-Snedecor diffusion. We propose a GMM approach to testing this statistical hypothesis where the moment condition is based on eigenfunctions of the diffusion infinitesimal generator-Fisher-Snedecor polynomials. Statistical test is observed in two different settings: (1) for known values of parameters of the process; (2) for consistent moment based estimators of parameters. Results are illustrated in a short simulation study.