﻿ 多元宏观时间序列的拟合及预测—基于VAR模型和状态空间模型 Fitting and Prediction of Multi Macroeconomic Time Series—Based on VAR Model and State-Space Model

Statistics and Application
Vol.05 No.02(2016), Article ID:17917,12 pages
10.12677/SA.2016.52013

Fitting and Prediction of Multi Macroeconomic Time Series

—Based on VAR Model and State-Space Model

Jingru Yin

College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming Yunnan

Received: Jun. 7th, 2016; accepted: Jun. 26th, 2016; published: Jun. 30th, 2016

ABSTRACT

Predictions have been concerned about the issue, especially in the macroeconomic. Univariate time series prediction can not meet basic needs. Multiple macroeconomic time series has urgent demand for reasonable model. Currently AR model and VAR model develop better, and to some extent, are used for analysis and policy analysis in macro fields. While state space model validates observable variables, unobserved variables are added. In an open economy and the rapid development background, state-space model can adapt to the actual needs. This paper selects the three basic macroeconomic variables in three areas (industrial, money supply and CPI), fitting VAR model and state space model and predicting, comparing predictions. The results show that the prediction accuracy of the state space model is superior to the VAR model.

Keywords:Prediction, State Space Model, VAR Model, Macroeconomic

—基于VAR模型和状态空间模型

1. 引言

2. 模型描述

2.1. 向量自回归(VAR)模型

Sims于1980年提出了向量自回归模型(简称VAR模型)，VAR模型不以经济理论为基础，采用多方程联立的形式，在模型的每一个方程中，内生变量对模型的全部内生变量的滞后值进行回归，进而估计全部内生变量的动态关系。VAR模型常用于预测相互联系的时间序列系统，也常用于分析随机扰动对变量系统的动态冲击，进而解释各种经济冲击对经济变量形成的影响 [3] 。

VAR模型的一般形式为：

(1)

(2)

VAR模型的特点有：首先，VAR模型不以经济理论为依据，在建模过程中只需要把那些相互有关的变量包括进VAR模型，同时确定滞后阶p即可；其次，VAR模型对待估计的参数施加零约束，即参数估计值不管显著与否，都保留在模型中；再次，VAR模型需要估计的参数较多，如一个含有三个变量，最大滞后期p = 3的VAR模型，有27个参数需要估计，所以当样本容量较小时，会严重影响VAR模型参数估计量的精度 [4] 。

2.2. 向量自回归移动平均(VARMAX)模型

(3)

，则为VARX模型：

(4)

2.3. 状态空间模型

(5)

(6)

(7)

3. 数据介绍

4. 实证检验

4.1. 数据描述

4.2. 协整检验

4.2.1. 平稳性检验

KPSS单位根检验结果如下表1所示。

4.2.2. 协整分析

Johansen协整检验结果如下表2表3所示：(分别用迹检验和最大特征值检验)

(1) 迹检验的检验统计量和临界值的输出见表2

Figure 1. Trend chart of M2 growth, the growth rate of industrial added value and CPI

Figure 2. Trend chart of M2 growth, the growth rate of industrial added value and CPI growth

Table 1. KPSS test results

Table 2. Values of trace test statistic and 10%, 5% and 1% critical values of test

(2) 最大特征值检验的检验统计量和临界值的输出见表3

EG协整检验：我们针对数据中的三个变量轮流做因变量来进行回归，结果三个回归方程的p值均小于0.01，表示回归都是显著的，也就是说变量之间有显著的相关关系。进而检验残差是否是 (0)的。结果如下表4所示。

Granger因果检验：结果如下表5所示。

4.3. VAR模型

Table 3. Values of eigen test statistic and 10%, 5% and 1% critical values of test

Table 4. The stability test of residuals of Engle-Granger test

Table 5. Granger causality testing results

(8)

VAR模型对2015年10个月的预测值与真实值的比较如表6所示。

4.4. VARX模型

(9)

Figure 3. Using VAR model to fit the three variables (M2 growth, the growth rate of industrial added value and CPI) data and making predictions for the coming months

Figure 4. The real value of the three variables (M2 growth, the growth rate of industrial added value and CPI)

Table 6. VAR model predictions and the real value (January 2015-October 2015)

(10)

Figure 5. Acf diagram and pacf diagram of residuals of results using VARX model to fit the three variables (M2 growth, the growth rate of industrial added value and CPI) data

2015年1月到2015年11月的预测值如表7所示。

4.5. 状态空间模型

(11)

(12)

5. 结论

Figure 6. Predictive value of M2 growth (dotted line)

Figure 7. Acf diagram and pacf diagram of residuals of results using state space model to fit the three variables (M2 growth, the growth rate of industrial added value and CPI) data

Table 7. VARX model predictions and the real value (January 2015-October 2015)

Table 8. State space model predictions and the real value (January 2015-October 2015)

Figure 8. Predictive value of M2 growth (dotted line)

Fitting and Prediction of Multi Macroeconomic Time Series—Based on VAR Model and State-Space Model[J]. 统计学与应用, 2016, 05(02): 136-147. http://dx.doi.org/10.12677/SA.2016.52013

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