一类由布朗运动驱动的滑动平均的参数矩估计

华东师范大学学报(自然科学版) ›› 2014, Vol. 2014 ›› Issue (4): 18-25.

一类由布朗运动驱动的滑动平均的参数矩估计

何伟平¹, 张世斌²

1. 内蒙古大学~~数学系, 呼和浩特010021;
2. 上海海事大学~~数学系, 上海201306

收稿日期:2013-09-01 修回日期:2013-12-01 出版日期:2014-07-25 发布日期:2014-07-25

Moment estimation for a class of moving averages driven by Brownian motions

HE Wei-ping¹, ZHANG Shi-bin²

1. Department of Mathematics, Inner Mongolia University, Hohhot} 010021, China; 2. Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China

Received:2013-09-01 Revised:2013-12-01 Online:2014-07-25 Published:2014-07-25

摘要/Abstract

摘要： 研究一类自相关结构具有周期性和递减性共存性质的由布朗运动驱动的滑动平均的参数矩估计.
通过研究模型参数与自协方差函数间的联系, 构造了参数的矩估计量.
借助滑动平均离散抽样过程谱密度的研究, 分析了其强混合系数的特点,
进而证明了该矩估计量的相合性和渐近正态性.
模拟显示估计量在小样本场合下也呈现良好的估计效果.
实例分析表明该模型可用于刻画船体应力随时间的变化情况.

关键词: 滑动平均, 相合性, 渐近正态性, 谱密度, \alpha-混合

Abstract: This paper was concerned with moment estimation for a
class of moving averages driven by Brownian motions, whose
autocorrelation functions take on both periodic and regressive
properties. Based on investigation of the relationship between the
parameter and auto-covariance function, the moment estimator of the
parameter was constructed. By analyzing the spectral density of the
discretely sampled trajectory, the properties of the mixing
coefficient were captured. Further, the consistency and asymptotic
normality of the estimator were proved. A simulation study showed
that the estimator achieves good performance even in the
small-sample circumstances. The real data analysis evidences that
the model can be used to depict the ship hull stress data.

Key words: moving average, consistency, asymptotic normality, spectral density, \alpha-mixing

中图分类号:

O212
O211.64

何伟平, 张世斌. 一类由布朗运动驱动的滑动平均的参数矩估计[J]. 华东师范大学学报(自然科学版), 2014, 2014(4): 18-25.

HE Wei-ping, ZHANG Shi-bin. Moment estimation for a class of moving averages driven by Brownian motions[J]. Journal of East China Normal University(Natural Sc, 2014, 2014(4): 18-25.

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