Distributions of the maximum likelihood and minimum contrast estimators associated with the fractional Ornstein-Uhlenbeck process

被引：0

作者：

Tanaka K. ^{[1
]}

机构：

[1] Department of Economics, Hitotsubashi University, Kunitachi

来源：

Statistical Inference for Stochastic Processes | 2013年 / 16卷 / 3期

基金：

日本学术振兴会;

关键词：

Characteristic function; Fractional Ornstein-Uhlenbeck process; Maximum likelihood estimator; Minimum contrast estimator; Unit root test;

D O I：

10.1007/s11203-013-9085-y

中图分类号：

学科分类号：

摘要：

We discuss some inference problems associated with the fractional Ornstein-Uhlenbeck (fO-U) process driven by the fractional Brownian motion (fBm). In particular, we are concerned with the estimation of the drift parameter, assuming that the Hurst parameter H is known and is in [1/2, 1). Under this setting we compute the distributions of the maximum likelihood estimator (MLE) and the minimum contrast estimator (MCE) for the drift parameter, and explore their distributional properties by paying attention to the influence of H and the sampling span M. We also deal with the ordinary least squares estimator (OLSE) and examine the asymptotic relative efficiency. It is shown that the MCE is asymptotically efficient, while the OLSE is inefficient. We also consider the unit root testing problem in the fO-U process and compute the power of the tests based on the MLE and MCE. © 2013 Springer Science+Business Media Dordrecht.

引用

页码：173 / 192

页数：19

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