ABC算法在MA(q)模型参数估计中的应用
Application of ABC Algorithm in Parameter Estimation of MA(q) Model
DOI: 10.12677/AAM.2019.83044, PDF,    科研立项经费支持
作者: 李玲慧, 陶倪杰, 张慧增：杭州师范大学理学院数学系，浙江 杭州
关键词: MA(q)模型；ABC算法；极大似然估计；MA(q) Model； ABC Algorithm； Maximum Likelihood Estimation
摘要: 本文利用近似贝叶斯计算给出了MA(q)模型的参数估计。在近似贝叶斯计算中，提高算法的抽样效率在于选取低维的包含参数信息尽可能多的统计量。在白噪声方差已知的情况下，本文采用前q阶样本自相关函数作为统计量。通过数值模拟进行比较，选用样本自相关函数远好于样本自协方差函数，大大提升了抽样的效率。在白噪声方差未知的情况下，采用前q阶样本自相关函数与样本方差作为统计量，分两步对参数进行近似贝叶斯估计。从数值模拟的效果来看，该方法大大提高了估计的精确度。
Abstract: In this paper, we provide the parameter estimation of the MA(q) model by using the approximate Bayesian computation. In the approximate Bayesian computation, a way to improve the sampling efficiency of the algorithm is choosing the statistics of low dimension, which contains as much in-formation of parameters as possible. As the variance of white noise is known, we use the sample autocorrelation function of the first q order as the statistics. Through the numerical simulations and comparison, effects of choosing the sample auto-correlation functions are much better than the sample auto-covariance function, which greatly improves the sampling efficiency. When the variance of white noise is unknown, we use the sample autocorrelation function of the first q order and the sample variance as statistics to realize a two-step approximation Bayesian parameter es-timation method. As a result of numerical simulation, this method greatly improves the accuracy of estimation.
文章引用：李玲慧, 陶倪杰, 张慧增. ABC算法在MA(q)模型参数估计中的应用[J]. 应用数学进展, 2019, 8(3): 389-399. https://doi.org/10.12677/AAM.2019.83044

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