一类由布朗运动驱动的滑动平均的参数矩估计

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

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.

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.