Autori
Es-Sebaiy, Khalifa
Es-Sebaiy, Mohammed

Titolo
Estimating drift parameters in a non-ergodic Gaussian Vasicek-type model
Periodico
Statistical methods & applications : Journal of the Italian Statistical Society
Anno: 2021 - Volume: 30 - Fascicolo: 2 - Pagina iniziale: 409 - Pagina finale: 436

We study a problem of parameter estimation for a non-ergodic Gaussian Vasicek-type model defined as dXt=θ(μ+Xt)dt+dGt, t≥0 with unknown parameters θ>0, μ∈R and α:=θμ, where G is a Gaussian process. We provide least square-type estimators (θ˜T,μ˜T) and (θ˜T,α˜T), respectively, for (θ,μ) and (θ,α) based a continuous-time observation of {Xt, t∈[0,T]} as T→∞. Our aim is to derive some sufficient conditions on the driving Gaussian process G in order to ensure the strongly consistency and the joint asymptotic distribution of (θ˜T,μ˜T) and (θ˜T,α˜T). Moreover, we obtain that the limit distribution of θ˜T is a Cauchy-type distribution, and μ˜T and α˜T are asymptotically normal. We apply our result to fractional Vasicek, subfractional Vasicek and bifractional Vasicek processes. This work extends the results of El Machkouri et al. (J Korean Stat Soc 45:329–341, 2016) studied in the case where μ=0.



SICI: 1618-2510(2021)30:2<409:EDPIAN>2.0.ZU;2-O

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