Estimation method of moving average model with missing data
Received date: 2018-03-04
Online published: 2020-04-29
针对含有多个连续缺失数据的滑动平均 MA($q$) 序列,基于 EM 算法得到其模型的参数估计, 并给出了序列缺失值估计及其协方差矩阵的表达式. 通过数值模拟验证了该算法的有效性, 同时得 到如下结论: 参数估计整体均方误差随着模型阶数的增加而增加, 随着模型特征根模长的增加而增加, 随着样本缺失比例的增加而增加, 随着序列长度的增加而减少. 对于缺失值估计整体均方误差而言, 随着 模型阶数的增加而增加, 随着模型特征根模长的增加而增加, 但对于序列长度与样本缺失比例并不敏感. 通过实例计算, 在缺失数据下该算法能够较好地给出 MA 模型的参数估计.
陈博, 何幼桦 . 缺失数据下滑动平均模型的估计方法[J]. 上海大学学报(自然科学版), 2020 , 26(2) : 181 -188 . DOI: 10.12066/j.issn.1007-2861.2035
Based on the EM algorithm for model parameter estimation, this paper examines the $q$-order moving average model with missing data, aiming at figuring out the estimation of missing data and its covariance matrix. The effectiveness of the proposed algorithm is verified by numerical simulation which shows the following results: the mean square error of the model parameter estimation grows with the increase of the model order, the length of model characteristic roots and the proportion of missing data respectively. In addition, the value decreases when the length of sequence increases. The mean square error of missing data grows with the increase of the model order and the length of model characteristic roots. However, it is not sensitive to the length of the sequence and the proportion of missing data. An instance illustrates that the method estimates the model well in the case of missing data.
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