Drift estimation for a periodic mean reversion process
Drift estimation for a periodic mean reversion process
复制标题
周期性均值回归过程的漂移估计
DOI：
10.1007/s11203-010-9045-8
复制
发表时间：
2010
影响因子：
0.8
通讯作者：
Thomas Kott
中科院分区：
文献类型：
--
作者：
H. Dehling;B. Franke;Thomas Kott
本文提出了一个周期均值回复的Ornstein-Uhlenbeck过程，其形式为
$$ dX_t=（L（t）-\alpha\，X_t）\，dt + \sigma\，dB_t，\quad t\geq 0，$$其中L（t）是周期参数函数。我们应用最大似然估计的漂移参数的基础上的时间连续观测。估计明确给出，我们证明了强一致性和渐近正态的观察期间数趋于无穷大。渐近研究的基本思想是将随机过程解释为在某个函数空间取值的随机变量序列。
AbstractIn this paper we propose a periodic, mean-reverting Ornstein–Uhlenbeck process of the form
$$ dX_t=(L(t)-\alpha\, X_t)\, dt + \sigma\, dB_t, \quad t\geq 0, $$where L(t) is a periodic, parametric function. We apply maximum likelihood estimation for the drift parameters based on time-continuous observations. The estimator is given explicitly and we prove strong consistency and asymptotic normality as the observed number of periods tends to infinity. The essential idea of the asymptotic study is the interpretation of the stochastic process as a sequence of random variables that take values in some function space.