样本自相关系数与偏自相关系数的研究

Study on the Sample Autocorrelation Coefficient and Partial Autocorrelation Coefficient

探讨了自相关系数(AC)、偏自相关系数(PAC)和样本相关系数(SAC)、样本偏相关系数(SPAC)的特性,并利用均匀分布产生随机数验证SAC和SPAC渐进服从正态分布的特性,自相关系数在时间序列数据建模中有重要应用,利用时间序列模型自回归滑动平均(ARMA)模型,模拟得到一组样本数据,求得各自的SAC和SPAC,分析ARMA模型的阶数不同时SAC和SPAC的差异,最后利用SAC和SPAC的特征对实际经济数据消费物价指数(CPI)进行建模,根据拟合优度显示拟合效果很好。

The autocorrelation coefficient （ AC ）, the partial autocorrelation coefficient （ PAC ）, the sample autocorrelation coefficient（SAC） ,and the sample partial autocorrelation coefficient（SPAC） were studied in this paper, which have an important application in time series modeling. To verify the SAC and SPAC are normal distributions, the uniform distribution was used to get randomnumbers, the ARMA（p, q） model was used which generated random numbers to analyze the difference between the SAC and SPAC. At last, the SAC and SPAC were used to model the real economic data CPI and the fitting results are very good.