时间序列均值和方差函数的确定方法

METHOD FOR DETERMINING FUNCTIONS OF TIME SERIES MEAN AND VARIANCE

发现并提出一个重要定理 :时间序列的方差与该序列的差分绝对值序列的趋势项具有相同的函数形式。在此基础上 ,建立一种确定该差分绝对值序列趋势项的方法 ,该方法首先采用样本周期图和多点平均对趋势项中的周期项和非周期项进行分离 ,分别求得其函数表达式 ,然后再综合得到整个趋势项函数 ,进而求得原时间序列的方差函数形式 ,其中待定参数可根据相关系数平稳序列理论求得。该方法也可用于确定时间序列的均值函数 (趋势项 )

A new theorem is presented, which points out that the variance of time series has the same functional form as the trend term of absolute value series of difference of the time series. Based on the discovery, a method for determining the trend term of the series is established, which obtains the periodic function of the trend term by the sample periodogram and the nonperiodic function of the trend term by multiple-point averaging, then the integral function of the trend term can be synthesized. The variance functional form of the original series can be derived from the trend function and its parameters obtained by the correlation coefficient stationary theory. This method can also be used to determine the mean function of time series.