1、计量经济学时间序列计量经济模型计量经济学时间序列计量经济模型思考题10.5解：判断变量之间是否具有协整关系可以对变量做基于回归残差的协整检验。首先检验变量的单整次数，然后在所有变量的单整次数相同的情况下，利用OLS法作协整回归，用OLS法对协整回归方程进行估计，得到残差序列，最后对于残差序列进行平稳性的检验。如果最后验证残差序列是平稳的，则说明变量之间存在协整关系，反之，则说明变量之间不具有协整关系。10.6解：若变量之间存在协整关系，则表明变量之间存在着长期稳定的关系，这种长期稳定的关系在短期动态过程的不断调整下得以维持。即相互协整的变量，虽然都是在一阶差分后平稳，受长期分量的支配，但是这些
2、变量通过线性组合，使得其中的长期变量可以互相抵消，从而产生平稳的时间序列。而误差修正机制是一种调节过程，反映短期的调节，防止相互协整过程长期关系的偏差在规模或数量上的扩大，从而得到协整后的平稳时间序列。误差修正模型的特点：（1）使用一阶差分项，消除了变量可能存在的趋势因素，从而避免了虚假回归问题和消除了可能的多重共线性问题；（2）引入了误差修正项，保证误差修正项为平稳序列，同时避免了变量水平值被忽视；（3）可以利用经典的回归方法对误差修正模型进行估计，而且可以使用通常的t检验与F检验来检验各变量的滞后项，直到选出最佳形式。练习题10.1解：（1）建立Eviews文件，生成利润（R）和红利（H）
3、的数据，做出散点图如下：利润的散点图红利的散点图从图中可以看出，利润和红利序列的均值和方差均不稳定，不是常数，是随着时间变化的，直观认为利润和红利序列都是非平稳的时间序列。（2）对利润序列进行单位根检验，由于利润序列具有截距，选择具有截距，滞后长度为1的ADF检验，得出的结果如下：Null Hypothesis: R has a unit rootExogenous: ConstantLag Length: 1 (Fixed)t-StatisticProb.*Augmented Dickey-Fuller test statistic-1.5738080.4916Test critical v
4、alues:1% level-3.5083265% level-2.89551210% level-2.584952*MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(R)Method: Least SquaresDate: 12/02/14 Time: 19:56Sample (adjusted): 1980Q3 2001Q4Included observations: 86 after adjustmentsVariableCoefficientStd
5、. Errort-StatisticProb.R(-1)-0.0349270.022192-1.5738080.1193D(R(-1)0.1770210.1067741.6579020.1011C5.9829883.0902321.9360970.0563S.E. of regression9.676572Akaike info criterion7.411553Sum squared resid7771.791Schwarz criterion7.497170Log likelihood-315.6968Hannan-Quinn criter.7.446010Durbin-Watson st
6、at2.003376从单位根检验可以看出，此时DW值为2.003376，与2很接近，而t统计量的值为-1.573808，大于所有显著性水平下的MacKinnon临界值，故不能拒绝原假设，该序列是非平稳的。同样的，对红利序列进行单位根检验，由于红利序列具有截距，选择具有截距，滞后长度为2的ADF检验，得出的结果如下：Null Hypothesis: H has a unit rootExogenous: ConstantLag Length: 2 (Fixed)t-StatisticProb.*Augmented Dickey-Fuller test statistic0.6719890.990
7、9Test critical values:1% level-3.5092815% level-2.89592410% level-2.585172*MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(H)Method: Least SquaresDate: 12/02/14 Time: 20:03Sample (adjusted): 1980Q4 2001Q4Included observations: 85 after adjustmentsVariab
8、leCoefficientStd. Errort-StatisticProb.H(-1)0.0033040.0049170.6719890.5035D(H(-1)0.6252350.1104025.6632580.0000D(H(-2)-0.1560710.111084-1.4049880.1638C0.4916800.3711211.3248480.1889R-squared0.326704Mean dependent var1.355294Adjusted R-squared0.301768S.D. dependent var1.930489S.E. of regression1.6131
9、22Akaike info criterion3.840136Sum squared resid210.7753Schwarz criterion3.955084Log likelihood-159.2058Hannan-Quinn criter.3.886371F-statistic13.10126Durbin-Watson stat2.087329Prob(F-statistic)0.000000从单位根检验可以看出，此时DW值为2.087329，与2很接近，而t统计量的值为0.671989，大于所有显著性水平下的MacKinnon临界值，故不能拒绝原假设，该序列是非平稳的。应用单位根检验
10、可以判断，利润和红利都是非平稳的时间序列。10.5解：（1）建立Eviews文件，生成中国财政收入对数（LnY）和税收对数（LnX）的数据做出LnY的散点图如下：对LnY序列进行单位根检验，由于中国财政收入对数序列具有截距，选择具有截距，滞后长度为2的ADF检验，得出的结果如下：Null Hypothesis: LNY has a unit rootExogenous: ConstantLag Length: 2 (Fixed)t-StatisticProb.*Augmented Dickey-Fuller test statistic2.3600660.9999Test critical v
11、alues:1% level-3.6891945% level-2.97185310% level-2.625121*MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(LNY)Method: Least SquaresDate: 12/02/14 Time: 20:14Sample (adjusted): 1981 2008Included observations: 28 after adjustmentsVariableCoefficientStd.
12、Errort-StatisticProb.LNY(-1)0.0268160.0113632.3600660.0267D(LNY(-1)0.5624550.2002432.8088610.0097D(LNY(-2)-0.3897620.204182-1.9088970.0683C-0.1170960.079861-1.4662470.1556R-squared0.553094Mean dependent var0.141711Adjusted R-squared0.497230S.D. dependent var0.063960S.E. of regression0.045351Akaike i
13、nfo criterion-3.217192Sum squared resid0.049362Schwarz criterion-3.026878Log likelihood49.04069Hannan-Quinn criter.-3.159011F-statistic9.900837Durbin-Watson stat1.971818Prob(F-statistic)0.000196从单位根检验可以看出，此时DW值为1.971818，与2很接近，而t统计量的值为2.360066，大于所有显著性水平下的MacKinnon临界值，故不能拒绝原假设，该序列是非平稳的。对LnY进行一阶差分后的单位根
14、检验，选择具有截距，滞后长度为2的ADF检验结果如下：Null Hypothesis: D(LNY) has a unit rootExogenous: ConstantLag Length: 2 (Fixed)t-StatisticProb.*Augmented Dickey-Fuller test statistic-2.5769380.1099Test critical values:1% level-3.6998715% level-2.97626310% level-2.627420*MacKinnon (1996) one-sided p-values.Augmented Dick
15、ey-Fuller Test EquationDependent Variable: D(LNY,2)Method: Least SquaresDate: 12/02/14 Time: 20:19Sample (adjusted): 1982 2008Included observations: 27 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.D(LNY(-1)-0.4623820.179431-2.5769380.0169D(LNY(-1),2)0.2177120.2065601.0539900.3028D(L
16、NY(-2),2)-0.1965350.210069-0.9355740.3592C0.0702120.0255572.7472900.0115S.E. of regression0.048763Akaike info criterion-3.067754Sum squared resid0.054689Schwarz criterion-2.875778Log likelihood45.41468Hannan-Quinn criter.-3.010670Durbin-Watson stat2.060016从单位根检验可以看出，此时DW值为2.060016，与2很接近，而t统计量的值为-2.5
17、76938，大于所有显著性水平下的MacKinnon临界值，故不能拒绝原假设，一阶差分后的序列仍是非平稳的。对LnY进行二阶差分后的单位根检验，选择具有截距，滞后长度为1的ADF检验结果如下：Null Hypothesis: D(LNY,2) has a unit rootExogenous: ConstantLag Length: 1 (Fixed)t-StatisticProb.*Augmented Dickey-Fuller test statistic-5.0199760.0004Test critical values:1% level-3.6998715% level-2.9762
18、6310% level-2.627420*MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(LNY,3)Method: Least SquaresDate: 12/02/14 Time: 20:22Sample (adjusted): 1982 2008Included observations: 27 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.D(LNY(-1),2)-1.
19、4358130.286020-5.0199760.0000D(LNY(-1),3)0.4174350.2131321.9585790.0619C0.0092200.0107150.8604980.3980S.E. of regression0.054191Akaike info criterion-2.888177Sum squared resid0.070479Schwarz criterion-2.744195Log likelihood41.99039Hannan-Quinn criter.-2.845364Durbin-Watson stat2.030166从单位根检验可以看出，此时D
20、W值为2.030166，与2很接近，而t统计量的值为-5.019976，小于99%显著性水平下的MacKinnon临界值，故拒绝原假设，认为二阶差分后的序列是平稳的，即LnYI（2）（2）做出LnX的散点图如下：对LnX序列进行单位根检验，由于税收对数序列具有截距，选择具有截距，滞后长度为1的ADF检验，得出的结果如下：Null Hypothesis: LNX has a unit rootExogenous: ConstantLag Length: 1 (Fixed)t-StatisticProb.*Augmented Dickey-Fuller test statistic0.205705
21、0.9682Test critical values:1% level-3.6793225% level-2.96776710% level-2.622989*MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(LNX)Method: Least SquaresDate: 12/02/14 Time: 20:31Sample (adjusted): 1980 2008Included observations: 29 after adjustmentsVar
22、iableCoefficientStd. Errort-StatisticProb.LNX(-1)0.0041110.0199850.2057050.8386D(LNX(-1)0.0218950.1965940.1113700.9122C0.1211150.1670560.7249940.4749R-squared0.002523Mean dependent var0.159081Adjusted R-squared-0.074206S.D. dependent var0.132402S.E. of regression0.137227Akaike info criterion-1.03666
23、8Sum squared resid0.489610Schwarz criterion-0.895224Log likelihood18.03169Hannan-Quinn criter.-0.992369F-statistic0.032882Durbin-Watson stat2.016928Prob(F-statistic)0.967693从单位根检验可以看出，此时DW值为2.016928，与2很接近，而t统计量的值为0.205705，大于所有显著性水平下的MacKinnon临界值，故不能拒绝原假设，该序列是非平稳的。对LnX进行一阶差分后的单位根检验，选择具有截距的DF检验结果如下：Nu
24、ll Hypothesis: D(LNX) has a unit rootExogenous: ConstantLag Length: 0 (Fixed)t-StatisticProb.*Augmented Dickey-Fuller test statistic-5.1189860.0003Test critical values:1% level-3.6793225% level-2.96776710% level-2.622989*MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(LNX,2)Method: Least SquaresDate: 12/02/14 Time: 20:33Sample (adjusted): 1980 2008Included observations: 29 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.
