基于总体最小二乘的AR(p)模型及其在建筑物沉降预测中的应用

摘要

为了研究时间序列理论中自回归AR(p)模型,采用最小二乘方法求解模型参数时未考虑数据相关性的问题,引进总体最小二乘这种能够处理系数矩阵和观测矩阵同时存在偶然误差的平差方法,将总体最小二乘平差准则用于自回归AR(p)模型的参数解算,讨论了AR(p)模型的阶数p的确定方法.结合建筑物沉降数据的分析与预测结果,表明基于总体最小二乘准则的时间序列分析方法得出的模型更加准确,短期预测效果更好.%In order to study the problem that in autoregressive AR (p ) model of time series the data dependence did not consider when solving the parameters of autoregressive model by least-squares method,the total least squares method is introduced, and this adjustment method can handle random errors both in coefficient matrix and observation matrix, the total least squares adjustment criteria is applied to solve the parameters of autoregressive AR(p) model,and the method to determine the order of p in AR(p) model is discussed.Combined with the analysis and predicted results of building subsidence, it shows that the model obtained by time series analysis based on total least squares adjustment criteria are more accurate, and the prediction effect in short term is well.