Estimating Drift Parameters in a Sub-Fractional Vasicek-Type Process

Anas D Khalaf; Tareq Saeed; Reman Abu-Shanab; Waleed Almutiry; Mahmoud Abouagwa

doi:10.3390/e24050594

Estimating Drift Parameters in a Sub-Fractional Vasicek-Type Process

Entropy (Basel). 2022 Apr 24;24(5):594. doi: 10.3390/e24050594.

Authors

Anas D Khalaf¹, Tareq Saeed², Reman Abu-Shanab³, Waleed Almutiry⁴, Mahmoud Abouagwa⁵

Affiliations

¹ General Directorate of Education in Saladin, Ministry of Education, Tikrit 34001, Iraq.
² Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia.
³ Mathematics Department, College of Science, University of Bahrain, Sakhir P.O. Box 32038, Bahrain.
⁴ Department of Mathematics, College of Science and Arts in Ar Rass, Qassim University, Buryadah 52571, Saudi Arabia.
⁵ Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt.

Abstract

This study deals with drift parameters estimation problems in the sub-fractional Vasicek process given by dxt=θ(μ−xt)dt+dStH, with θ>0, μ∈R being unknown and t≥0; here, SH represents a sub-fractional Brownian motion (sfBm). We introduce new estimators θ^ for θ and μ^ for μ based on discrete time observations and use techniques from Nordin−Peccati analysis. For the proposed estimators θ^ and μ^, strong consistency and the asymptotic normality were established by employing the properties of SH. Moreover, we provide numerical simulations for sfBm and related Vasicek-type process with different values of the Hurst index H.

Keywords: Berry–Esseen; Vasicek-type model; central limit theorem; parameter estimation; strong consistency.

Publication types

Review