﻿ 基于ARIMA模型的河南省全社会固定资产投资预测分析 Forecast and Analysis of Fixed Assets Investment in Henan Province Based on ARIMA Model

Statistics and Application
Vol.06 No.05(2017), Article ID:23245,8 pages
10.12677/SA.2017.65066

Forecast and Analysis of Fixed Assets Investment in Henan Province Based on ARIMA Model

Mao Yang, Changchun Wang

Henan University of Technology, Zhengzhou Henan

Received: Dec. 8th, 2017; accepted: Dec. 22nd, 2017; published: Dec. 29th, 2017

ABSTRACT

ARIMA model can solve the modeling problem of non-stationary time series well, and it has a good application time in the short-term prediction of time series model. By collecting the data from 1989 to 2014, combined with EVIEWS software, finally, the ARIMA model is applied to the analysis and forecast of the total investment of fixed assets in Henan province. The results show that the ARIMA model can be used to analyze the total assets of Henan province. The results show that the model can solve the problem of estimating and forecasting the investment of fixed assets in Henan province, and the prediction accuracy is high so as to provide the government with a fixed asset investment ratio and the amount of investment to provide a reliable reference to promote the healthy development of the economy.

Keywords:Henan Province, Whole Society Fixed Asset Investment, Time Series Analysis, ARIMA Forecast

ARIMA模型能较好的解决非平稳时间序列的建模问题，并且在时间序列模型的短期预测方面有很好的应用时间，文章通过搜集从1989年~2014年的数据，结合EVIEWS软件，建立河南省全社会固定资产投资总额自回归移动平均模型ARIMA (p, d, q)的时间序列模型并进行检验，最后将ARIMA模型应用于河南省全社会固定资产投的资总额分析及预测。结果表明，该模型能较好的解决河南省全社会固定资产投资的估计和预测问题，预测精度较高。从而为政府提供固定资产投资比例和投资金额提供可靠的参考依据，促进经济的健康发展。

1. 引言

2. 序列的平稳性检验

2.1. 原序列的平稳性检验

Figure 1. Timing chart of total fixed assets investment in Henan from 1989 to 2014

2.2. 对数序列的平稳性检验

$\left\{{y}_{t}\right\}$ 序列作单位根检验，原假设： ${H}_{0}:|\lambda |\ge 1$ ；备择假设： ${H}_{1}:|\lambda |<1$ ，检验结果如表2所示。

2.3. 序列 $\left\{{y}_{t}\right\}$ 的差分处理

Table 1. ADF test results of the sequence Y

Figure 2. Autocorrelation-partial autocorrelation diagram

Figure 3. xt timing diagram

3. 模型建立

$\text{ARIMA}\left(p,d,q\right)$ 模型的识别与定阶可以通过样本的自相关与偏自相关函数的观察获得 [3] 。经过平稳性检验，我们建立 $\text{ARIMA}\left(p,d,q\right)$ ，模型经过一阶差分后平稳，所以 $d=1$ ，为了获得自回归和移动平均回归中的 $p$$q$ ，可以通过自相关和偏自相关图来观察。图4$\left\{{x}_{t}\right\}$ 序列的自相关图和偏自相关图。

$\begin{array}{l}{x}_{t}=0.199550+0.507968{x}_{t-1}-0.082020{\epsilon }_{t-1}-0.887127{\epsilon }_{t-5}+{\epsilon }_{t}\\ t=\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(15.76010\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(2.452251\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(-0.939909\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(-14.49139\right)\end{array}$

$\text{S}\text{.E}\text{.}=0.055682$ , ${R}^{2}=0.688939$ , ${\stackrel{¯}{R}}^{2}=0.642279$ , $F=14.76533$

$\text{AIC}=-2.787294$ , $\text{SC}=-2.590951$ , $\text{DW}=2.089939$

${y}_{t}={y}_{t-1}+0.199550+0.507968{x}_{t-1}-0.082020{\epsilon }_{t-1}+{\epsilon }_{t}$

$Y={\text{e}}^{{y}_{t-1}+0.199550+0.507968{x}_{t-1}-0.082020{\epsilon }_{t-1}+{\epsilon }_{t}}$

Figure 4. xt autocorrelation-partial autocorrelation of sequences

Table 4. Comparison of different ARMA ( p , q ) model AIC and SC values

Figure 5. First-order difference model $\text{ARIMA}\left(1,1,5\right)$ of the total social investment in fixed assets

4. 模型的检验

5. 模型的预测

Table 5. Residual LM test results

Table 6. Estimated total investment in fixed assets of Henan province from 2015 to 2018 (Unit: 100 million Yuan)

Figure 6. Residual sequence autocorrelation-partial autocorrelation analysis

Figure 7. Real and static estimates of total fixed assets investment in Henan province

Forecast and Analysis of Fixed Assets Investment in Henan Province Based on ARIMA Model[J]. 统计学与应用, 2017, 06(05): 583-590. http://dx.doi.org/10.12677/SA.2017.65066

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