摘要
本文在简单介绍ARMA(p,q)模型识别方法的基础上,推导了ARMA(p,q)模型向AR(p1)模型转换的方法。然后介绍了最小二乘法(LS)在AR模型参数估计中的应用,并指出了该方法的缺陷:在进行参数的估计时,只考虑了当期观测值的误差而并没有顾及系数矩阵的误差。在此基础上,将整体最小二乘(TLS)法引入到AR模型的参数求解中,详细介绍了TLS的解算方法。最后通过对具体工程实例的变形监测数据的分析,验证了采用了TLS法对AR模型参数估计及预报的可行性,并且比LS法具有更高的精度。
Based on recognizing method of the ARMA （p, q） model, this paper proposed a method to transform ARMA （p, q） to AR （Pl）. Through the analyzing of the least squares （LS） in AR model, we find that only the errors of current observations are considered, but no consideration of errors in coefficient matrix. Therefore, the total least squares （TLS） is inducted into the determination of AR model parameters. Finally, we use real deformation monitoring data to verify the feasibility of solving AR model parameters and forecasting by using TLS method, the results demonstrate that TLS method is more accurate than LS method.
出处
《工程勘察》
2013年第12期41-43,65,共4页
Geotechnical Investigation & Surveying
基金
国家自然科学基金(41174012
41274022)
关键词
AR模型
变形监测
奇异值分解法
整体最小二乘
AR model
deformation monitoring
singular value decomposition
total least square
