1、一阶差分检验结果检验形式(C,T,L)ADF值P值P值*Lcpi(C,0,12)-2.102780.2440(0,0,11)-5.23850.0000Lm(C,T,0)-0.090940.9947(C,0,0)-13.278shibor(C,T,1)-3.23630.0810-14.317Lindex-1.638920.4605(0,0,1)-7.0603注:检验形式(C,T,L)中,C,T,L分别代表常数项、时间趋势和滞后阶数。滞后阶数根据SC信息准则选择。从表中可以看出,在5的显著性水平上,所有变量均不平稳,但是一阶差分均平稳,因此所有变量均是一阶单整过程。3、协整检验协整检验的关键是选取
2、协整检验的形式和滞后阶数。根据前面介绍的协整与VECM模型的关系,协整方程根据数据特征分成三类。由于部分变量存在截距和趋势,因此选取第二类形式。考虑到cpi、上证指数无明显的时间特征,因此选取第三种形式作为协整检验的形式。对于滞后阶数的选取,可以根据VAR滞后阶数间接选取或者根据信息准则选取,同时考虑残差的性质。当滞后阶数为1时,AIC和SC分别为-15.75672、-15.23181;当滞后阶数为2时,AIC和SC分别为-15.76829、-14.94004;当滞后阶数为3时,AIC和SC分别为-15.75608、-14.62198。另外估计无约束的VAR模型时滞后阶数小于5时各判断准则的结
3、果优于高阶的情形。因此本例中滞后阶数选取为1。在Group窗口中点击view/cointegration test,选取形式三和滞后区间(1 1)。具体协整检验的结果见下。协整检验的结果:Sample (adjusted): 1997M02 2010M11Included observations: 166 after adjustmentsTrend assumption: Linear deterministic trendSeries: LCPI LINDEX LM SHIBORLags interval (in first differences): 1 to 1Unrestricte
4、d Cointegration Rank Test (Trace)HypothesizedTrace0.05No. of CE(s)EigenvalueStatisticCritical ValueProb.*None *0.18010066.6873547.856130.0003At most 1 *0.12799033.7242029.797070.0168At most 20.04805110.9898115.494710.2121At most 30.0168172.8153253.8414660.0934Trace test indicates 2 cointegrating eqn
5、(s) at the 0.05 level* denotes rejection of the hypothesis at the 0.05 level*MacKinnon-Haug-Michelis (1999) p-valuesUnrestricted Cointegration Rank Test (Maximum Eigenvalue)Max-Eigen32.9631527.584340.009222.7343921.131620.02958.17448214.264600.3612Max-eigenvalue test indicates 2 cointegrating eqn(s)
6、 at the 0.05 level迹检验和极大特征值检验结果均显示存在两个协整关系。再分析具体的协整方程和协整序列。标准化后的协整方程如下。2 Cointegrating Equation(s):Log likelihood1347.175Normalized cointegrating coefficients (standard error in parentheses)LCPILINDEXLMSHIBOR1.0000000.000000-0.033542-0.010324(0.00927)(0.00237)-0.135405-0.297467(0.31487)(0.08046)第二个协
7、整方程显示lm与shibor之间是负相关关系,这与一般的经济理论相悖,本例只选取一个协整方程。协整序列的图形和单位根检验结果如下。Null Hypothesis: COINTEQ has a unit rootExogenous: Constant, Linear TrendLag Length: 0 (Automatic based on SIC, MAXLAG=13)t-StatisticProb.*Augmented Dickey-Fuller test statistic-3.5511910.0373Test critical values:1% level-4.0146355% le
8、vel-3.43728910% level-3.142837*MacKinnon (1996) one-sided p-values.协整方程所对应的序列是平稳的,即各变量之间存在协整关系。该协整方程具体为:4、VECM模型的估计估计结果如下:Standard errors in ( ) & t-statistics in Cointegrating Eq:CointEq1LCPI(-1)LINDEX(-1)-0.105613(0.04668)-2.26233LM(-1)-0.019242(0.03646)-0.52780SHIBOR(-1)0.021093(0.00768) 2.74693C
9、-3.657863Error Correction:D(LCPI)D(LINDEX)D(LM)D(SHIBOR)-0.0193870.059896-0.018894-1.234481(0.00578)(0.08100)(0.00619)(0.32963)-3.35440 0.73942-3.05460-3.74500D(LCPI(-1)0.0922040.368908-0.2839250.140230(0.07718)(1.08179)(0.08261)(4.40219) 1.19460 0.34102-3.43713 0.03185D(LINDEX(-1)-0.0004560.0928070
10、.008193-0.329584(0.00571)(0.08000)(0.00611)(0.32554)-0.07985 1.16012 1.34121-1.01242D(LM(-1)-0.112222-0.152122-0.0600074.609028(0.07009)(0.98235)(0.07501)(3.99752)-1.60113-0.15486-0.79997 1.15297D(SHIBOR(-1)0.0018600.018777-0.001956-0.169503(0.00133)(0.01870)(0.00143)(0.07609) 1.39387 1.00418-1.3702
11、1-2.227550.0016000.0090280.014056-0.129375(0.00106)(0.01492)(0.00114)(0.06071) 1.50275 0.60511 12.3372-2.13088R-squared0.1163370.0166520.1120420.110396Adj. R-squared0.088722-0.0140780.0842930.082596Sum sq. resids0.0060131.1811970.00688719.56028S.E. equation0.0061300.0859210.0065610.349645F-statistic
12、4.2128950.5418724.0377413.971055613.1981174.9293601.9309-58.04941Akaike AIC-7.315639-2.035293-7.1798900.771680Schwarz SC-7.203158-1.922812-7.0674080.884161Mean dependent-4.57E-050.0064620.013460-0.059337S.D. dependent0.0064220.0853230.0068560.365046Determinant resid covariance (dof adj.)1.39E-12Dete
13、rminant resid covariance1.20E-121335.808Akaike information criterion-15.75672Schwarz criterion-15.231815、VECM模型的检验与预测在VAR估计窗口中点击view/residual tests/cointegration test观察各方程对应残差的自相关图。(此处不显示不同残差之间的相关图,VECM模型允许不同残差之间存在相关性)从中可以看出,除lindex存在一定的自相关性外,其余均不存在自相关性。与VAR模型类似,VECM模型的估计窗口中无直接预测的命令。要对VECM模型进行预测,需由估
14、计的VECM模型建立Model得到。点击proc/make model,打开model窗口,在VECM方程下编辑命令:Assign all _f表示对所有的变量的预测值名后加上后缀名_f。各变量采用确定模拟中动态方案预测的结果对比图如下。从中可以看出VECM模型基本可以拟合原序列的变动趋势。6、VECM模型的应用在VAR估计的窗口,点击view/impulse response查看脉冲响应函数。选择combined graphs可以得到脉冲响应的组合图显示结果。从左上方的图形可以看出,股指的变动对货币供给在中长期内都存在影响,而货币供给对股票市场的影响很小。点击view/variance de
15、composition查看方差分解结果。ombined graphs可以得到脉冲响应的组合图显示结果。从右上方的图形可以看出,股指的变动主要源于自身的影响,因此股指变量具有弱外生性。而货币供给的变动短期内自身影响较大,中长期内股票市场的变动和物价的变动会逐渐增强,两者的影响和达到将近30。7、施加约束条件后的VECM的估计可以对协整向量或者VECM模型的系数施加约束条件,一方面可以检验系数是否真正显著,另外还可以对变量之间的关系进行检验,如因果关系。本例中,点击view/representations,可以查看VECM模型的方程形式,如下:D(LCPI) = A(1,1)*(B(1,1)*LC
16、PI(-1) + B(1,2)*LINDEX(-1) + B(1,3)*LM(-1) + B(1,4)*SHIBOR(-1) + B(1,5) + C(1,1)*D(LCPI(-1) + C(1,2)*D(LINDEX(-1) + C(1,3)*D(LM(-1) + C(1,4)*D(SHIBOR(-1) + C(1,5)D(LINDEX) = A(2,1)*(B(1,1)*LCPI(-1) + B(1,2)*LINDEX(-1) + B(1,3)*LM(-1) + B(1,4)*SHIBOR(-1) + B(1,5) + C(2,1)*D(LCPI(-1) + C(2,2)*D(LINDEX
17、(-1) + C(2,3)*D(LM(-1) + C(2,4)*D(SHIBOR(-1) + C(2,5)D(LM) = A(3,1)*(B(1,1)*LCPI(-1) + B(1,2)*LINDEX(-1) + B(1,3)*LM(-1) + B(1,4)*SHIBOR(-1) + B(1,5) + C(3,1)*D(LCPI(-1) + C(3,2)*D(LINDEX(-1) + C(3,3)*D(LM(-1) + C(3,4)*D(SHIBOR(-1) + C(3,5)D(SHIBOR) = A(4,1)*(B(1,1)*LCPI(-1) + B(1,2)*LINDEX(-1) + B(
18、1,3)*LM(-1) + B(1,4)*SHIBOR(-1) + B(1,5) + C(4,1)*D(LCPI(-1) + C(4,2)*D(LINDEX(-1) + C(4,3)*D(LM(-1) + C(4,4)*D(SHIBOR(-1) + C(4,5)如在协整方程中货币供给量(lm)不显著,可以剔除lm后重新估计VECM方程。从上面的方程可以看出,lm对应的回归系数为b(1,3),因此在VECM估计窗口中点击VEC restrictions,输入b(1,3)=0,得到新的VECM估计方程如下。 Cointegration Restrictions:B(1,3)=0Convergenc
19、e achieved after 13 iterations.Not all cointegrating vectors are identifiedLR test for binding restrictions (rank = 1):Chi-square(1)0.114241Probability0.7353678.315332-1.3371810.297447-29.32485-0.0015350.006492-0.001447-0.107336(0.00048)(0.00668)(0.00051)(0.02709)-3.20789 0.97169-2.82184-3.962150.0900730.446647-0.284004-0.385101(0.07775)(1.08530)(0.08331)(4.40082) 1.15851 0.41154-3.40889-0.08751-0.0002670.0924540.008384-0.318814(0.00572)(0.07989)(0.00613)(0.32394)-0.04662 1.15730 1.36707-0.98418-0.106557-0.146748-0.0538444.844492(0.07014)(0.97914)(0.07516)(3.97035)-1.51912-0.14987-0.71635 1.
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