A pathwise inference method for the parameters of diffusion terms

Abstract

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.

Parameter estimation in CKLS model by continuous observations

“…For the case of CIR process, the problem of the drift parameters estimation was extensively studied in the literature, see e. g. Ben Kebaier (2012, 2013); De Rossi (2010); Dehtiar et al (2021); Overbeck and Rydén (1997) and references cited therein. However in the case β = 1/2 we can mention only the work by Dokuchaev (2017), who studied the estimation of the diffusion term parameters β and σ.…”

Fast maximum likelihood estimation of parameters for square root and Bessel processes

“…Their estimates, based on discrete-time observations, are derived from conditional least squares estimates of modified parameters, assuming that the diffusion parameter σ is known. On the other hand, in Dokuchaev (2017) estimators of σ are supplied that do not require knowledge of the drift parameters. In Overbeck and Rydén (1997), estimators of parameters of (3), employing observations at equispaced times and based on conditional least squares, are studied.…”