VAR模型总结与Eviews实现.doc

一 案例说明对中国1990-2007年的进出口贸易总额进行分析，数据如下：YearExportImportYearExportImport19902985.82574.3199916159.813736.419913827.13398.7200020634.418638.819924676.34443.3200122024.420159.219935284.85986.2200226947.924430.3199410421.89960.1200336287.934195.6199512451.811048.1200449103.346435.8199612576.411557.4200562648.154273.7199715160.711806.5200677594.663376.9199815223.611626.1200793455.673284.6二 VaR建模2.1 探索性分析如图所示，中国进出口数据具有较强的相关性，因此适用于建立VaR模型。2.2 建立VaR模型如上图所示建立VaR模型，结果如下表所示：Date: 04/21/10 Time: 11:00Sample (adjusted): 1992 2007Included observations: 16 after adjustmentsStandard errors in ( ) & t-statistics in EXPORTIMPORTEXPORT(-1)0.193423-0.898005(0.53677)(0.63778) 0.36035-1.40801EXPORT(-2)0.3485250.842249(0.53421)(0.63473) 0.65242 1.32694IMPORT(-1)1.1587822.196035(0.42066)(0.49982) 2.75467 4.39365IMPORT(-2)-0.298354-0.894162(0.63098)(0.74971)-0.47284-1.19267C-1269.422-250.5640(959.091)(1139.57)-1.32357-0.21988R-squared0.9955610.990496Adj. R-squared0.9939470.987040Sum sq. resids4793638567674960S.E. equation2087.5472480.377F-statistic616.8156286.6099Log likelihood-142.0054-144.7641Akaike AIC18.3756718.72052Schwarz SC18.6171118.96195Mean dependent30040.7125934.93S.D. dependent26832.7021788.19Determinant resid covariance (dof adj.)7.99E+12Determinant resid covariance3.77E+12Log likelihood-277.0800Akaike information criterion35.88500Schwarz criterion36.36787从表中可以看出，VaR模型可以解释99%的方差，因此该模型比较合理。2.3 滞后阶数选择选择Views-Lag Structure-Lag Length Criteria，弹出对话框，如下选择：得结果如下：VAR Lag Order Selection CriteriaEndogenous variables: EXPORT IMPORTExogenous variables: CDate: 04/21/10 Time: 11:02Sample: 1990 2007Included observations: 15LagLogLLRFPEAICSCHQ0-310.1213NA4.06e+1541.6161741.7105841.615171-262.162076.73483*1.17e+13*35.75494*36.03816*35.75192*2-260.40712.3399481.65e+1336.0542836.5263136.049253-256.43234.2397621.83e+1336.0576436.7184936.05060* indicates lag order selected by the criterionLR: sequential modified LR test statistic (each test at 5% level)FPE: Final prediction errorAIC: Akaike information criterionSC: Schwarz information criterionHQ: Hannan-Quinn information criterion从结果可以看出，选择滞后阶数为1比较合理，从而应该重新建立VAR模型，步骤同2.2，结果如下：Date: 04/21/10 Time: 11:04Sample (adjusted): 1991 2007Included observations: 17 after adjustmentsStandard errors in ( ) & t-statistics in EXPORTIMPORTEXPORT(-1)0.419366-0.513030(0.24454)(0.30497) 1.71492-1.68226IMPORT(-1)0.9613531.773317(0.28565)(0.35623) 3.36555 4.97804C-880.4163235.7087(718.770)(896.378)-1.22489 0.26296R-squared0.9955540.989585Adj. R-squared0.9949190.988097Sum sq. resids5088922479145976S.E. equation1906.5532377.664F-statistic1567.527665.0772Log likelihood-150.8735-154.6275Akaike AIC18.1027718.54441Schwarz SC18.2498018.69145Mean dependent28498.7424609.27S.D. dependent26747.2421792.90Determinant resid covariance (dof adj.)6.58E+12Determinant resid covariance4.46E+12Log likelihood-295.8150Akaike information criterion35.50765Schwarz criterion35.801732.4 VAR模型平稳性检验点击Views-Lag Structure-AR Roots Graph功能，可以得单位圆曲线和VAR模型特征根的结果。该VAR模型中单位根都大于1， 因此是一个非平稳系统。2.5 VAR模型预测在VAR模型估计结果的窗口中点击Proc-Make Model，可以得到模型，点击Solve，在出现的对话框中进行选择就可以得到对应的预测值。其中动态解可以预测出序列的变化趋势，但对具体年份的预测效果不好；静态解对数据的拟合程度比较好。如果要进行样本外预测，需要激活工作页面，点击Procs-Change Workfile Range将样本区间扩展，在进行对应操作即可得到样本外预测。2.6 脉冲响应和方差分解脉冲响应方差分解2.7 协整检验点击View-Cointergration Test，即可打开Johansen Cointergtation Test对话框结果如下所示：Date: 04/21/10 Time: 11:40Sample (adjusted): 1992 2007Included observations: 16 after adjustmentsTrend assumption: Linear deterministic trendSeries: EXPORT IMPORTLags interval (in first differences): 1 to 1Unrestricted Cointegration Rank Test (Trace)HypothesizedTrace0.05No. of CE(s)EigenvalueStatisticCritical ValueProb.*None0.53206713.1788215.494710.1084At most 10.0622261.0279383.8414660.3106Trace test indicates no cointegration 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)HypothesizedMax-Eigen0.05No. of CE(s)EigenvalueStatisticCritical ValueProb.*None0.53206712.1508814.264600.1051At most 10.0622261.0279383.8414660.3106Max-eigenvalue test indicates no cointegration at the 0.05 level* denotes rejection of the hypothesis at the 0.05 level*MacKinnon-Haug-Michelis (1999) p-valuesUnrestricted Cointegrating Coefficients (normalized by b*S11*b=I):EXPORTIMPORT0.000364-0.0006150.000840-0.000957Unrestricted Adjustment Coefficients (alpha):D(EXPORT)-1682.757183.1770D(IMPORT)-1183.706445.97411 Cointegrating Equation(s):Log likelihood-277.5939Normalized cointegrating coefficients (standard error in parentheses)EXPORTIMPORT1.000000-1.692372(0.13759)Adjustment coefficients (standard error in parentheses)D(EXPORT)-0.611962(0.18273)D(IMPORT)-0.430474(0.22092)2.8 VEC模型结果如下：Date: 04/21/10 Time: 11:41Sample (adjusted): 1992 2007Included observations: 16 after adjustmentsStandard errors in ( ) & t-statistics in Cointegrating Eq:CointEq1EXPORT(-1)1.000000IMPORT(-1)-1.692372(0.13759)-12.3004C12060.57Error Correction:D(EXPORT)D(IMPORT)CointEq1-0.611962-0.430474(0.18273)(0.22092)-3.34905-1.94851D(EXPORT(-1)-0.218450-0.525560(0.37043)(0.44787)-0.58972-1.17347D(IMPORT(-1)0.1244020.470647(0.37599)(0.45458) 0.33087 1.03534C6147.6785030.046(1773.98)(2144.81) 3.46548 2.34522R-squared0.9017150.719084Adj. R-squared0.8771440.648855Sum sq. resids4847324670857247S.E. equation2009.8352429.973F-statistic36.6981510.23913Log likelihood-142.0945-145.1317Akaike AIC18.2618118.64147Schwarz SC18.4549618.83461Mean dependent5601.7834367.866S.D. dependent5734.0674100.702Determinant resid covariance (dof adj.)7.16E+12Determinant resid covariance4.02E+12Log likelihood-277.5939Akaike information criterion35.94924Schwarz criterion36.43211三 VAR理论考虑具有内生向量和外生向量的系统，称其满足VAR模型，如果有误差向量允许变量之间相关，但这些误差变量不能存在自相关(事实上自相关可以通过增加滞后阶数消除，因此该要求也不甚严格)。VAR模型对于相互联系的时间序列变量系统是有效的预测模型，同时，向量自回归模型也被频繁地用于分析不同类型的随机误差项对系统变量的动态影响。3.1 VAR模型如果变量之间不仅存在滞后影响，而不存在同期影响关系，则适合建立VAR模型，因为VAR模型实际上是把当期关系隐含到了随机扰动项之中。一般的k元p阶VAR模型如下式所示：上式可以简写为其中，L为滞后算子。如果模型满足平稳性条件，根据Wold定理可将其表示