多维相关系数平稳序列分析方法

相关系数平稳序列是从非平稳随机序列中分离出来的一类工程上常见且又便于研究的一类时间序列,其均值和方差都可随时间变化,因此,与传统平稳过程相比,它能更好地描述工程中的时间序列.在相关系数平稳过程的基础上,给出多维相关系数平稳过程的定义,建立了新的多维相关系数序列的理论和方法,给出了多维相关系数序列的极大似然估计.通过对时域的全程分析,能够充分利用样本信息对相关系数序列的均值函数,协方差矩阵函数和相关系数矩阵函数进行估计.在此基础上,对多维相关系数平稳序列进行高精度的频谱分析.

Analysis method of multi-dimensional correlation coefficient stationary series

The correlation coefficient stationary series is one kind of non-stationary series is familiar in egineering,and its mean and variance can vary with time.The traditional stationary process is just a special case of it.Then,it can describe the time series better.On the basis of correlation coefficient stationary process,this paper gives the definition of multi-dimensional correlation coefficient steady process and introducts the series of multi-dimensional correlation coefficient steady process.New theories and methods are established for multi-dimensional correlation coefficient series and the paper gives its MLE.Wiht making full use of the information contained in data,the mean function,variance matrix function and correlation coefficient matrix function of multi-dimensional correlation coefficient series can be obtained by the present method.On this basis,we can carry out the spectral analysis with high precision.