ASYMPTOTIC THEORY FOR ESTIMATING DRIFT PARAMETERS IN THE FRACTIONAL VASICEK MODEL
研究了分数维Vasicek模型中两个漂移参数的估计渐近性质，针对持续参数的不同符号（平稳、爆炸、零常返）分别给出了最小二乘估计的强相合性和渐近分布，对金融利率建模研究者有参考价值。
This article develops an asymptotic theory for estimators of two parameters in the drift function in the fractional Vasicek model when a continuous record of observations is available. The fractional Vasicek model with long-range dependence is assumed to be driven by a fractional Brownian motion with the Hurst parameter greater than or equal to one half. It is shown that, when the Hurst parameter is known, the asymptotic theory for the persistence parameter depends critically on its sign, corresponding asymptotically to the stationary case, the explosive case, and the null recurrent case. In all three cases, the least squares method is considered, and strong consistency and the asymptotic distribution are obtained. When the persistence parameter is positive, the estimation method of Hu and Nualart (2010) is also considered.