Asymptotic distribution of the maximum likelihood estimator in the fractional Vašíček model

Maximum likelihood estimation in the non-ergodic fractional Vasicek model

“…We start with the bivariate MGF of the vector (S T , I T ). For the case β > 0, it was derived in [26,Lemma 3.3]. However, the same proof is valid for the case β < 0.…”

“…Remark 3. Unlike the ergodic case (studied in[26]), in the non-ergodic case the initial value x 0 affects the asymptotic bias of β T . If β < 0, then the deterministic term…”

Maximum Likelihood Estimation in the Mixed Fractional Vasicek Model

“…The Vasicek model is used in finance, economics, biology, physics, chemistry, medicine , environmental studies and in other areas for modeling purposes. In a series of papers, Lohvinenko and Ralchenko [12,13,14,15] studied asymptotic properties of the maximum likelihood estimators of the parameters α and β in the fractional Vasicek model…”

“…Remarks: Even though the form of the function k H (t, s) is known, due to its complicated form, it is not possible to use the methods in Lohvinenko and Ralchenko [12,13,14,15] to study the asymptotic distribution of (α T ,β T ) or the asymptotic marginal distributions ofα T and β T after suitable scaling as T → ∞. However, following ideas in Lohvinenko and Ralchenko [13], we will transform the problem to the study of maximum likelihood estimation for the parameters of sub-fractional Vasicek model to that of estimation of parameters for a subfractional Ornstein-Uhlenbeck process (Mendy [16], Yu [41], Es-Sebaiy-Es-sebaiy [7], Xiao et al [37] ) and derive the asymptotic properties of the corresponding MLE.…”

“…Properties of fractional Vasicek model for modeling are investigated in Chronopoulu and Viens [2], Corlay et al [3], Hao et al [8], Song and Li [30] and Xiao et al [37] among others. Maximum likelihood estimation for fractional Vasicek model is investigated in Lohvinenko and Ralchenko [12,13,14,15] and Xiao and Yu [38,39].…”