摘要
传统的基于相关性分析方法进行建模的局限性和"危险性"主要表现在:估计的样本自相关是非常坏的估计,经常会有大的方差,彼此之间是高度相关的,可能给出原来序列结构一个完全失真的图像,不能较准确和全面地反映系统特性。提出了基于动态数据系统的时间序列建模方法,将时间序列看作是随机系统对不相关的或相互独立的"白噪声"输入响应的一种实现方式。对平稳时间序列,以自回归滑动平均模型为基本模型,并以额值为1递增拟合,用F检验判断拟合的改善程度,最后用残差分析判断模型的适用性。对非平稳序列,需先分离出确定性趋势,对剩余平稳随机部分建模分析。用该方法对隧道位移监测数据建模分析,预测与实测吻合较好,表明该方法具有适用性好、精度高且便于编制程序实现等优点。
The limitations and ＂risks＂ existing in traditional modelling methods based on correlation analysis mainly lies in the following three areas： estimated sample autocorrelation is a poor estimator with regular large variance and high relationships with each other; they may produce a completely distorted image of the original series structure; and they are unable to reflect system characteristics accurately and roundly. A modelling method based on dynamic data systems in time series was presented. The time series was regarded as a realistic way to input response on a stochastic system to uncorrelated white noise. For stationary time series, an autoregressive moving average model was the basic model. The model took 1 as the increasing amplitude and fits model, used the F test to judge the degree to which the fit improved, and used residue analysis to weigh model applicability. For nonstationary time series, it needed to isolate deterministic trends first, and then model and analyze the surplus remaining stochastic portion. This method was used to model and analyze the displacement monitoring data of tunnels. The prediction accorded well with actual measurements. The results show that the method is quite applicable, highly precise, and can be easily implemented through programs.
出处
《重庆大学学报（自然科学版）》
CAS
CSCD
北大核心
2008年第5期558-562,共5页
Journal of Chongqing University
基金
国家自然科学基金资助项目(50374084)
关键词
时间序列
动态数据系统
建模策略
最小二乘估计
线性回归
time series
dynamic data system
modeling strategy
least squares approximations
linear regression
