Estimation of all parameters in the reflected Orntein-Uhlenbeck process from discrete observations

2020/09/10 by Yaozhong Hu, Hu, Yaozhong, Yuejuan Xi +1
Mathematics · #62F12 #62M05 #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #msc:62F12 #msc:62M05 #stat.TH

paper · pdf · doi:10.48550/arxiv.2009.05162

arxiv created 2020/09/10 · arxiv updated 2020/09/14

Abstract

Assuming that a reflected Ornstein-Uhlenbeck state process is observed at discrete time instants, we propose generalized moment estimators to estimate all drift and diffusion parameters via the celebrated ergodic theorem. With the sampling time step h > 0 arbitrarily fixed, we prove the strong consistency and asymptotic normality of our estimators as the sampling size n tends to infinity. This provides a complete solution to an open problem left in Hu et al. [5].

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