确定时间序列协方差函数的方法

提出一种确定时间序列协方差函数的方法,它首先根据(多元)时间序列构造其互协方差函数随机序列、互相关函数随机序列或自协方差函数随机序列、自相关函数随机序列,然后采用谱分析和多点平均方法对互协方差函数随机序列、互相关函数随机序列或自协方差函数随机序列、自相关函数随机序列的趋势项进行分离,分别求得其周期项和非周期项的函数表达式,再综合给出整个趋势项函数。从而得到原时间序列的互协方差函数、互相关函数或自协方差函数、自相关函数的函数形式,并通过最小二乘方法确定其中的待定参数。该方法可用于时间序列协方差函数的建模、分析和预测,并且计算简单易行、精度高,便于实际应用。

Method for Determining Covariance Functions of Time Series

A method for determining covariance functions of time series is presented.First,it can construct a series of cross covariance,cross correlation,auto-covariance or auto-correlation function according to the time series.Then,it can determine the trend term of the cross covariance,the cross correlation,the auto-covariance or the auto-correlation function series,which obtains not only the periodic function of the trend term by the spectral analysis but also the nonperiodic function by multiple-point averaging,and synthesizes the integral function of the trend term.The functional form of the cross covariance,the cross correlation,the auto-covariance or the auto-correlation function can be derived from the trend function.Besides,its parameters are estimated by the least squares method.The presented method is credible and easily available for modeling,analysis and forecast of the covariance and the correlation function of time series.