论文标题
在高频观测下，分数布朗运动的准可能性分析恒定漂移
Quasi-Likelihood Analysis of Fractional Brownian Motion with Constant Drift under High-Frequency Observations
论文作者
论文摘要
考虑（0,1）$的Hurst参数$ h \ in（0,1）$的估计，而波动率参数$σ> 0 $，用于分数布朗运动，并在高频观察下具有有限的时间间隔，并在高频观察下进行漂移术语。在本文中，我们提出了一个一致的参数$θ=（h，σ）$的一致估计器，结合了基于局部高斯高斯近似高频率观察到的频率时间序列及其频域近似值的局部高斯函数的想法。此外，当漂移过程恒定时，我们证明了所有$ h \ in（0,1）$的拟议估计量的渐近正态性属性。
Consider an estimation of the Hurst parameter $H\in(0,1)$ and the volatility parameter $σ>0$ for a fractional Brownian motion with a drift term under high-frequency observations with a finite time interval. In the present paper, we propose a consistent estimator of the parameter $θ=(H,σ)$ combining the ideas of a quasi-likelihood function based on a local Gaussian approximation of a high-frequently observed time series and its frequency-domain approximation. Moreover, we prove an asymptotic normality property of the proposed estimator for all $H\in(0,1)$ when the drift process is constant.
