A pathwise inference method for the parameters of diffusion terms

Nikolai Dokuchaev

Journal of Nonparametric Statistics, 2017, vol. 29, issue 4, 731-743

Abstract: We consider inference of the parameters of the diffusion term for continuous time stochastic processes with a power-type dependence of the diffusion coefficient from the underlying process such as Cox–Ingersoll–Ross, CKLS, and similar processes. 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.

Date: 2017
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DOI: 10.1080/10485252.2017.1367789

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