相关系数ARMA(p,q)序列分析方法

本文提出相关系数ARMA(p,q)序列分析方法。相关系数ARMA(p,q)序列是从非平稳序列中分离出的一类工程上常见且便于研究的时间序列,在模式识别、故障诊断、信号处理、自动控制和结构响应分析等领域有着广泛的应用。传统的相关函数ARMA(p,q)序列仅是它的一个特例。文中建立了相关系数ARMA(p,q)序列的条件极大似然估计和精确极大似然估计,前者在样本较大时简单便于工程应用,后者则在样本较小时仍具有较高的精度,它们通过时域的全程分析,充分利用样本信息确定相关系数ARMA(p,q)序列的均值函数、方差函数和相关系数函数。在此基础上可进行高精度的频谱分析。

Analysis Method of Correlation Coefficient ARMA(p,q) Series

The correlation coefficient ARMA(p,q)series of which mean and variance may vary with time is widely used in engineering,such as pattern recognition,fault diagnosis,signal processing,automatic control,structure response analysis and so on.The traditional correlation function stationary ARMA(p,q) model is just a special case of that.The conditional maximum likelihood estimation (MLE) and exact MLE for the correlation coefficient ARMA(p,q) series are established in this paper,which can obtain its mean function,variance function and correlation coefficient function with high precision.The conditional MLE is simple and convenient for engineering application when the sample is large enough,and the exact MLE is still precise in the case of small sample. Base on analyzing in time domain,the spectral analysis of correlation coefficient ARMA(p,q) series can be done.