# 关于我国物价水平的时间序列分析Time Series Analysis of China’s Price Level

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CPI指数ARIMA(pdq)模型预测CPI Index ARIMA(pdq) Model Forecast

This paper analyzes the CPI index of China from 1985 to 2014 by using time series measurement model. First, the data is analyzed in a stationary manner. It is found that the sequence has an increasing trend through the sequence diagram, so the sequence is a non-stationary sequence . The sequence is processed by logarithmic process and the first order difference is made. The basic stability is found by the sequence diagram after the difference. Then the ARIMA(p,d,q) model is fitted to the stationary sequence. The fitting effect test and the heteroscedasticity test of the model are carried out . Finally, the fitting model is used to predict the CPI data of the next 5 years. It can be seen from the prediction results that the CPI is still increasing.

1. 研究背景、意义及目的

2. 模型介绍

$\left\{\begin{array}{l}\varphi \left(B\right){\Delta }^{d}{x}_{t}=\theta \left(B\right){ϵ}_{t}\\ E\left({ϵ}_{t}\right)=0,\text{\hspace{0.17em}}Var\left({ϵ}_{t}\right)={\sigma }_{ϵ}^{2},\text{\hspace{0.17em}}E\left({\epsilon }_{t}{ϵ}_{s}\right)=0,\text{\hspace{0.17em}}s\ne t\\ E\left({\epsilon }_{S}{ϵ}_{t}\right)=0,\text{\hspace{0.17em}}\forall s

${\Delta }^{d}{x}_{t}=\underset{i=0}{\overset{d}{\sum }}{\left(-1\right)}^{i}{C}_{d}^{i}{x}_{t-i}$

$\Delta {x}_{t}={\gamma }_{1}{x}_{t-1}+\dots +{\gamma }_{p}{x}_{t-p}+{ϵ}_{t},\text{\hspace{0.17em}}\text{\hspace{0.17em}}t=1,2,\cdots ,T$ (1)

$\Delta {x}_{t}=\mu +{\gamma }_{1}{x}_{t-1}+\cdots +{\gamma }_{p}{x}_{t-p}+{ϵ}_{t},\text{\hspace{0.17em}}\text{\hspace{0.17em}}t=1,2,\cdots ,T$ (2)

$\Delta {x}_{t}=\mu +\beta t+{\gamma }_{1}{x}_{t-1}+\cdots +{\gamma }_{p}{x}_{t-p}+{ϵ}_{t},\text{\hspace{0.17em}}\text{\hspace{0.17em}}t=1,2,\cdots ,T$ (3)

${\text{H}}_{0}:{\gamma }_{1}=0$

${\text{H}}_{1}:{\gamma }_{1}\ne 0$

3. 数据来源

4. 实证分析

4.1. 数据处理

Figure 1. 1985-2014 national CPI index (1978 = 100)

Figure 2. 1985-2014 data on the logarithmic data of the national CPI index

Figure 3. First order difference data

4.2. 随机性检验

4.3. 平稳性检验

Figure 4. ACF inspection figure

Figure 5. PACF inspection figure

4.4. 模型拟合

${x}_{t}={x}_{t-1}+{\epsilon }_{t}+0.8186{\epsilon }_{t-1}$

4.5. 模型的显著性检验

4.6. 预测

Figure 6. CPI forecast for 2015-2020

5. 结论

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