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Parameter estimation for fractional Ornstein-Uhlenbeck processes at discrete observation

机译:离散观测中分数阶Ornstein-Uhlenbeck过程的参数估计

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摘要

This paper deals with the problem of estimating the parameters for fractional Ornstein-Uhlenbeck processes from discrete observations when the Hurst parameter H is known. Both the drift and the diffusion coefficient estimators of discrete form are obtained based on approximating integrals via Riemann sums with Hurst parameter H∈(1/2,3/4). By adapting the stochastic integral representation to the fractional Brownian motion, these two estimators can be efficiently computed by the use of computer software. Numerical examples are presented to examine the performance of our method. An application to real data is also presented to show how to apply this method in practice.
机译:本文讨论了在已知赫斯特参数H的情况下从离散观测值估计分数Ornstein-Uhlenbeck过程的参数的问题。基于具有Hurst参数H∈(1 / 2,3 / 4)的Riemann和,通过近似积分获得离散形式的漂移和扩散系数估计。通过使随机积分表示适应分数布朗运动,可以通过使用计算机软件来有效地计算这两个估计量。数值例子被提出来检验我们方法的性能。还介绍了对实际数据的应用,以展示如何在实践中应用此方法。

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