Estimation of all parameters in the reflected Ornstein–Uhlenbeck process from discrete observations

2022

Preprint

We study the Nadaraya-Watson (N-W) estimator for the drift function of twosided reflected stochastic processes. We propose a discrete-type N-W estimator and a continuous-type N-W estimator based on the discretely observed processes and continuously observed processes respectively. Under some regular conditions, we obtain the consistency and establish the asymptotic distributions for the two estimators. Furthermore, we briefly remark that our method can be applied to the one-sided reflected stochastic processes spontaneously.Numerical studies show that the proposed estimators is adequate for practical use.

Section: Introductionmentioning

confidence: 99%

Nadaraya-Watson estimator for reflected stochastic processes driven by Brownian motions

Han¹,

2022

Preprint

“…An ergodic type estimator for drift parameters based on discretely observed reflected O-U processes is proposed in [11]. Subsequently, an ergodic type estimator for all parameters (drift and diffusion parameters) is proposed in [13]. However, there is only limited literature on the drift parameter estimation of nonlinear reflected SDEs.…”

Section: Introductionmentioning

confidence: 99%

Drift parameter estimation for nonlinear reflected stochastic differential equations

Han¹,

2022

Preprint

We study the maximum likehood estimator and least squares estimator for drift parameters of nonlinear reflected stochastic differential equations based on continuous observations. Under some regular conditions, we obtain the consistency and establish the asymptotic distributions of the two estimators. We briefly remark that our methods could be applied the the reflected stochastic processes with only one-sided reflecting barrier spontaneously. Numerical studies show that the proposed estimators are adequate for practical use.

“…For discretely observed reflected O-U processes, an ergodic type estimator for drift parameters is proposed by [14]. Subsequently, an ergodic type estimator for all parameters (drift and diffusion parameters) was proposed by [16]. For nonlinear stochastic processes, [18] proposed a NLSE for the drift parameter of discretely observed stochastic processes driven by a standard Brownian motion and give its strong consistency.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Least Squares Estimator for Discretely Observed Reflected Stochastic Processes

Han¹,

2022

Preprint

We study the problem of parameter estimation for reflected stochastic processes driven by a standard Brownian motion. The estimator is obtained using nonlinear least squares method based on discretely observed processes. Under some certain conditions, we obtain the consistency and establish the asymptotic normality of the estimator. Moreover, we briefly remark that our method can be extended to the one-sided reflected stochastic processes spontaneously. Numerical studies show that the proposed estimator is adequate for practical use.