A pathwise inference method for the parameters of diffusion terms. Issue 4 (2nd October 2017)

• Record Type: Journal Article
• Authors: Dokuchaev, Nikolai
• Is Part Of: Journal of nonparametric statistics. Volume 29:Issue 4(2017)
• Page Start: 731
• Page End: 743
• Publication Date: 2017-10-02
• Subjects: Diffusions processes -- volatility -- power index -- pathwise estimation -- Cox–Ingersoll–Ross process -- CKLS model; C14 -- C15 -- C58; 91G70 -- 65C30 -- 65C50 -- 65C60; Nonparametric statistics -- Periodicals; 519.5
• DOI: 10.1080/10485252.2017.1367789
• Languages: English
• ISSNs: 1048-5252

Abstract

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.