统计研究 ›› 2010, Vol. 27 ›› Issue (9): 97-102.

• 论文 • 上一篇    下一篇

基于ARFIMA(p, d, q)过程的半参数估计量分布特征及其有偏性研究7737976300

邓露   

  • 收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2010-09-15 发布日期:2010-09-15

The Distribution Characteristic and Bias of Semi-parametric Estimator Based on an ARFIMA(p, d, q) Process

Deng Lu   

  • Received:1900-01-01 Revised:1900-01-01 Online:2010-09-15 Published:2010-09-15

摘要: 本文运用蒙特卡罗模拟的方法对小样本下长记忆性的三种半参数估计量的分布特征尤其是有偏性问题进行了深入分析,结果发现,当长记忆和短记忆同时存在时,在大多数情况下,各参数估计量仍然服从正态分布,因此在小样本下仍可以构造t统计量判别参数的显著性,但由于受到短期参数的影响,估计量的分布是有偏的,因此导致参数的估计和检验出现偏差。而当真实数据过程接近非平稳或过度差分时,半参数估计量的分布也会发生改变。

关键词: 长记忆, 半参数估计量, 有偏性, 蒙特卡罗模拟

Abstract: This paper used the Monte-Carlo simulation method to analyze the distribution characteristic and bias of three semi-parametric estimators of long memory in finite samples. It turned out that in most situations, each estimator has the distribution of normality and a t statistics can be formed to test its significance when long memory and short memory exist at the same time. However, affected by the short term parameter, the distributions are biased so that the estimators and the following t test are less believable. In addition, when the true data process is near nonstationary or over-differencing, the distribution of estimators in finite sample is changed.

Key words: Long, Memory, Semi-parametric, Estimator, Bias, Monte-Carlo, Simulation