Estimating drift parameters in a non-ergodic Gaussian Vasicek-type model

2019/09/13 by Es-Sebaiy, Khalifa, Sebaiy, Mohammed Es.
#60G15 #60G22 #62F12 #62M09 #62M86 #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1909.06155

Abstract

We study the problem of parameter estimation for a non-ergodic Gaussian Vasicek-type model defined as dX_t=(μ+θX_t)dt+dG_t, t≥0 with unknown parameters θ>0 and μ∈ℝ, where G is a Gaussian process. We provide least square-type estimators \widetildeθ_T and \widetildeμ_T respectively for the drift parameters θ and μ based on continuous-time observations \X_t, t∈[0,T]\ as T→∞. Our aim is to derive some sufficient conditions on the driving Gaussian process G in order to ensure that \widetildeθ_T and \widetildeμ_T are strongly consistent, the limit distribution of \widetildeθ_T is a Cauchy-type distribution and \widetildeμ_T is asymptotically normal. We apply our result to fractional Vasicek, subfractional Vasicek and bifractional Vasicek processes. In addition, this work extends the result of \citeEEO studied in the case where μ=0.

Related

• Parameter estimation for Vasicek model driven by a general Gaussian noise
• Asymptotic properties of parameter estimators in Vasicek model driven by tempered fractional Brownian motion
• Statistical Estimations for Non-Ergodic Vasicek Model Driven by Two Types of Gaussian Processes
• Maximum likelihood estimation for sub-fractional Vasicek model
• Least squares estimator for non-ergodic Ornstein-Uhlenbeck processes driven by Gaussian processes