Abstract
In this paper, under discrete observations, we study Cramér-type moderate deviations (extended central limit theorem) for parameter estimation in Ornstein-Uhlenbeck process. Our results contain both stationary and explosive cases. For applications, we propose test statistics which can be used to construct rejection regions in the hypothesis testing for the drift coefficient, and the corresponding probability of type II error tends to zero exponentially. Simulation study shows that our test statistics have good finite-sample performances both in size and power. The main methods include the deviation inequalities for multiple Wiener-Itô integrals, as well as the asymptotic analysis techniques.
Highlights
The short rate Xt will deviate from average level much more drastically when θ > 0
Cramer-type moderate deviations are still missing in both stationary case and explosive case
Simulation study shows that our test statistics have good finite-sample performances both in size and power
Summary
Shimizu ([43]) obtained the asymptotic distribution of Kasonga’s estimator θn,Δ under this high frequency observations. Bercu et al ([5]), Bercu and Richou ([7]) obtained the large deviations for the maximum likelihood estimator of θ, while Jiang and Zhang ([27]) considered the Cramer-type moderate deviations. In the discrete observation case, Shimizu ([42]) proved the asymptotic normality for the maximum likelihood estimator of θ in the stationary case. Cramer-type moderate deviations are still missing in both stationary case and explosive case. Our motivation is to study the Cramer-type moderate deviations (so-called extended central limit theorem) for Kasonga’s estimator θn,Δ, and we handle both stationary case and explosive case. We benefit a lot from Gao et al ([19])
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