  We consider inference of the parameters of the diffusion term for
Cox-Ingersoll-Ross and similar processes with a power type dependence of the
diffusion coefficient from the underlying process. We suggest some original
pathwise estimates for this coefficient and for the power index based on an
analysis of an auxiliary continuous time complex valued process generated by
the underlying real valued process. These estimates do not rely on the
distribution of the underlying process and on a particular choice of the drift.
Some numerical experiments are used to illustrate the feasibility of the
suggested method.
