论文标题
离散观察到的分数迭代的Ornstein-uhlenbeck过程的建模和参数估计
Modelling and Parameter Estimation for Discretely Observed Fractional Iterated Ornstein--Uhlenbeck Processes
论文作者
论文摘要
我们扩展了赫斯特参数小于1/2的情况的任何fou（p）过程的理论结果，我们在理论上和模拟在T和样本大小n的某些条件下进行模拟，当时可以获得一致的参数估计值，当时可以在分配和equspaced间隔[0，t]中观察到该过程的一致估计值。我们还将证明，FOU（P）过程可用于建模广泛的时间序列，从短距离依赖到大范围依赖性，结果与ARMA或ARFIMA模型相似，并且在某些情况下，它们的表现优于这些。最后，我们提供了一种方法，以获取任何FOU（P）的自动协方差功能的显式公式，并提出了FOU（2）和FOU（3）的申请。
We extend the theoretical results for any FOU(p) processes for the case in which the Hurst parameter is less than 1/2 and we show theoretically and by simulations that under some conditions on T and the sample size n it is possible to obtain consistent estimators of the parameters when the process is observed in a discretized and equispaced interval [0, T ]. Also we will show that the FOU(p) processes can be used to model a wide range of time series varying from short range dependence to large range dependence with similar results as the ARMA or ARFIMA models, and in several cases outperforms those. Lastly, we give a way to obtain explicit formulas for the auto-covariance function for any FOU(p) and we present an application for FOU(2) and FOU(3).
