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1、居民消费价格指数的季节ARIMA模型及短期预测摘 要 本文是以居民消费价格指数CPI的短期预测为主线,采用定量的时间序列分析方法,建立季节自回归综合移动平均模型季节ARIMA模型对CPI进行定量分析,并用图、文、数相结合的方式来揭示经济变量CPI与时间变量之间的变动规律。本文的研究思路是运用季节ARIMA模型, 并提供使用这类模型进行建模及预报的一般过程,即：对数据进行平稳性检验、平稳化处理、模型的差分阶数识别、参数估计,建立时间序列模型,并对模型进行检验,确定较适合季节自回归综合移动平均模型,然后再进行预测分析。本文基于时间序列分析,对以1990为基期的我国CPI定基比数据进行了实证分析时间
2、长度为从1990年到2007年的216个月,最终确定较适合的季节自回归综合移动平均模型.利用该模型对我国20212021年CPI作出预测并与实际值比拟,结果说明相对误差均在1%之内,预测模型良好.结果说明, 季节ARIMA模型在短期内的预测结果是可以接受的, 平均相对误差e=0.00211, 说明预测的精度是比拟高的.但是随着预测期的延长, 预测的误差将逐渐增大, 反映在预测置信区间的宽度上, 表现于随着预测期的延长, 预测置信区间的宽度越大, 因此, 该模型适合短期预测。但是,本文也有缺乏之处.一是由于季节ARIMA模型只考虑时间序列本身的特性来预测.二是没有考虑到CPI数据还受许多不可预测
3、的复杂因素影响如国民经济的开展程度、利率水平、汇率水平、货币供给量等内在因素的影响, 而这些突然变化的因素在季节ARIMA模型中只能以随机扰动项来表示, 在预期的期望值中是无法表现出来的.因此, 利用季节ARIMA模型进行预测时应和实际情况结合综合考虑和分析。关键词：CPI;时间序列分析;季节ARIMA模型;数量研究Seasonal ARIMA Model for CPI Short Forecasting ABSTRACT This article,adopting quantitative time series analysis approaches,establishing the S
4、easonal Auto-regressive Integrated Moving Average Model (Seasonal ARIMA) for quantitative analysis of the Consumer Price Index(CPI) and using graphs,characters and algebra to reveal variation law between the CPI and the time variable, concentrates on the short-term forecasting of the CPI.Research id
5、eas of this article not only use the Seasonal ARIMA model but also provide the use of such models the general process of modeling and prediction,namely：stability test of the data,establishing the time series models,and testing the model to find out the more suitable parameters for Seasonal ARIMA mod
6、el,then the forecast.Based on time series analysis,this paper makes the empirical analysis(length of time from 1990 to 2007,216 months total) on the basis of the fixed base ratio CPI data whose base time is in 1990,and ultimately determine the more suitable Seasonal ARIMA model ARIMA(0,2,2)(0,1,1).T
7、hrough using this model to forecast CPI for 2021-2021 two years and compared with the actual values,results show that the relative error is within 1%,thus the prediction model is good.It also shows that the Seasonal ARIMA model predictions in the short-term is acceptable because the average relative
8、 error is just 0.00211 and the prediction accuracy is relatively high.However,with the extension of the forecast period,forecast error is on the rise,reflecting the width of the confidence interval in the forecast,the more extended forecast period,the greater the width of confidence interval predict
9、ion.Therefor,the model is barely suitable for short-term prediction.However,this paper also has its drawbacks.First,the Seasonal ARIMA model predicts just considering the time series characteristics.Second,this article does not take the CPI data which is also complicated by many unpredictable factor
10、s such as degree of development of the national economy,interest rates,exchange rates,money supply and other internal factors into consideration.These sudden changing factors in the Seasonal ARIMA model can only be represented by random disturbance term which does not show in anticipation of the exp
11、ected values.Therefore,combined the actual situation with the Seasonal ARIMA model to analysis and predict is indispensable.KeyWords:CPI;Time series analysis;Seasonal ARIMA model;Quantity research目 录一 引言1.1 CPI概述及其分析预测背景.1.2 本文的主要工作.二 时间序列分析根本理论. 2.1 模型的理论准备. 时间序列概述. 时间序列的理论根底. 2.1.3 时间序列的主要性质. 1平稳性. 2遍历性. 3白噪音过程. 2.2 时间序列根本模型. 自回归模型. 移动平均模型. 自回归滑动平均模型. 1自回归综合移动平均模型. 2季节自回归综合移动平均模型.三 时间序列分析的根本思路.3.1 时间序列的预处理. 平稳性检验. 1自相关分析. 2游程检验. 平稳化处理. 3.2 模型的识别. 根据自相关函数与偏自相关函数的初步定阶. 利用BIC准那么准确定阶.3.3 参数估计.3.4 模型检验. 四 基于时间序列模型的CPI预测实例分析.
