计量经济学-时间序列计量经济模型

1、计量经济学时间序列计量经济模型思考题解：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,得到残差序列为，最后对于残差序列出进行平稳性的检验。 如果最后验证残基仔列外是平稳的，则说明变后之间存在协整关系，反之，则说明变量之间 不具有协整关系。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卜得以维持。即相互协整的变最，虽然都是在一阶差分后 平稳，受长期分量的支配，但是这些变量通过线性组合，使得其中的

2、长期变量可以互相抵消， 从而产生平稔的时间序列。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）的数据，做出散点图

3、如卜.： 利涧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 ength: 1 (Fixed)t-StatisticProb *Augmented Dickey-Fuller test statistic-1.5738080.4916Test critical values:

4、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 adjustmentsVanableCoefficientStd. Error

5、 t-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 enter.7 446010Durbin-Watson stat2.003

6、376从单位根检验可以看出，此时DW值为2.003376,与2很接近，而t统计最的值为-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，选择具行截距，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-Statistic Prob *Augmented Dickey-Fuller test statistic0.6719890.9909Test

7、 entieal values:1 % level-3.5092815% level-2.89592410% level-2.585172MacKinnon (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 adjustmentsVariableCoef

8、ficientStd. Error t-StatisticProb.H(-D0.0033040.0049173.6719890 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.dependentvar1 930489S.E of regression1.613122Akaike

9、info critenon3 840136Sum squared resid210.7753Schwarz criterion3.955084Log likelihood-159.2058Hannan-Quinn enter.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。 应用单位根检验可以判断，利润和红

10、利都是非平稳的时间序列。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，由于中国财政收入而数序列具有截距，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 Dickcy-Fullcr test statistic2.3600660.9999Test critical values:1% leve

11、l-3.6891945% level10% level-2.971853-2.625121MacKinnon (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. Error t-Statis

12、ticProb.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. dependentvar0.063960S.E. of regression0 045351Akaike info criterion-

13、3.217192Sum squared resid0 049362Schwarz critenon-3 026878Log likelihood49,04069Hannan-Quinn enter.-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卜的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检验，选择具有假距，滞后长度为

14、2的ADF检验结果如卜.： Null Hypothesis. D(LNY) has a unit rootExogenous: ConstantLag Length: 2 (Fixed)t-Statistic Prob *Augmented Dickey-Fuller test statistic-2.5769380.1099Test critical values:1 % level5% level10% level-3.699871-2.976263-2.627420,MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller T

15、est EquationDependent Variable: D(LNYf2)Method: Least SquaresDate: 12/02/14 Time: 20 19Sample (adjusted): 1982 2008Included observations: 27 after adjustmentsVanableCoefficientStd. Errort-StatisticProbD(LNY(-1)-0 4623820.179431-2.5769380 0169D(LNY(-1).2)0.2177120.2065601.0539900 3028D(LNY(-2),2)-0.1

16、965350.210069-0.9355740.3592c0.0702120.0255572.7472900 0115S.E. of regression0.048763Akaike info criterion-3.067754Sum squared resid0.054689Schwarz critenon-2 875778Log likelihood4541468Hannan-Quinn enter.-3.010670Durtm-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-2.576938, 大于所有显著性水平下

17、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检验结果如卜.： Null Hypothesis. D(LNY,2) has a unit root Exogenous: Constant Lag Length: 1 (Fixed)t-StatisticProb*Augmented Dickey-Fuller test statistic-5.0199760.0004Test entieal values:1 % level-3.6998715% level-2.97626310% level-

18、2.627420eMacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(LNYf3)Method: Least SquaresDate: 12/02/14 Time: 20:22Sample (adjusted). 1982 2008Included observations: 27 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.D(LNY(-1),2)-1 4358130.2860

19、20-5.0199760 0000D(LNY(-1),3)0 4174350.2131321.9585790 0619c0.0092200.0107150.8604980.3980S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat0.054191 Akaike info critenon0.070479 Schwarz criterion41.99039 Hannan-Quinn enter.2 030166-2 888177-2.744195-2 845364从单位根检验可以看,出，此时DW值为2.03

20、0166,与2很接近，而t统计量的值为-5.019976, 小于99%显著性水平卜.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，BPLnY-l (2)为LnX序列进行单位根检验，由于税收对数序列具行截距，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 statistic0.2057050.9682Test cntic

21、al values:1% level-3.6793225% level-2.96776710% level-2.622989MacKinnon (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 adjustmentsVariableCoefficientSt

22、d. Errort-StatisticProb.LNX(-1)0.0041110.0199853.2057050.8386D(LNX(-1)0.0218950.1965949.1113700 9122C0.1211150.1670563.72499404749R-squared0 002523Mean dependent var0 159081Adjusted R-squared-0.074206S.D. dependentvar0.132402S.E. of regression Sum squared resid Log likelihood F-statistic-1.0366680 1

23、37227 Akaike info critenon0.489610 Schwarz criterion-0.89522418.03169 Hannan-Quinn enter.-0.992369Prob(F-statistic)0 9676930 032882 Durbin-Watson stat2 016928从单位根检验可以看出，此时DW值为2.016928,与2很接近，而t统计最的值为0.205705, 大于所有显著性水平卜的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：Null Hypothesis:

24、 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-2.622989MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D

25、(LNX,2)Method Least SquaresDate: 12/02/14 Time: 20:33Sample (adjusted): 1980 2008Included observations 29 after adjustmentsVariableCoefficientStd. Error t-StatisticProb.D(LNX(-1)-0.9704410.189577-5.1189860.0000C0.1545190.0385014.0133300.0004R-squared0.492520Mean dependent var0.004747Adjusted R-squar

26、ed0 473724S.D. dependent var0.185776S.E. of regression0.134771Akaike info critenon-1 104007Sum squared resid0.490407Schwarz criterion-1.009711Log likelihood18.00811Hannan-Quinn enter.-1.074475F-statistic26,20402Durbin-Watson stat2 018256从单位根检验可以在出，此时DW值为2.018256,与2很接近，而t统计量的值为-5.118986, 小于于99%显著性水平卜

27、.的MacKinnon临界值，故拒绝原假设，认为一阶差分后的序列是 平稳的，WLnX-l (1)由于InY和InX不是同阶单整的，故两者之间不存在协整关系。#?：(1)建立Eviews文件，生成实际人均年收入对数(5丫)和实际人均年消费支出对数(LnC)的数据做出LnY的散点图如下:对LnY序列进行单位根检验，由于实际人均年收入对数序列具有截距，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: LNY has a unit rootExogenous: ConstantLag Length: 1 (Fixed)t-StatisticProb*Augme

28、nted Dickey-Fuller test statistic2.7701631 0000Test critical values:1 % level-3.6104535% level-2.93898710% level-2.607932MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable. D(LNY)Method: Least SquaresDate: 12/02/14 Time: 20:44Sample (adjusted): 1952 1990Inclu

29、ded observations: 39 after adjustmentsVariableCoefficient Std. Error -Statistic Prob.LNY(-1)0.0667850.0241092.7701630.0088D(LNY(-1)-0 0581110.175921-0.3303250.7431C-0 3277530.135418-2.4203010 0207R-squared0.209652Mean dependent var0056880Adjusted R-squared0.165744S.D. dependentvar0.076424S.E. of reg

30、ression0.069804Akaike info criterion-2.412449Sum squared resid0 175413Schwarz criterion-2.284483Log likelihood50 04276Hannan-Quinn enter-2 366536-statistic4 774770Durbin-Watson stat2.009457从单位根检验可以看出，此时DW值为2.009457,与2很接近，而t统计量的值为2.770163,大于所有显著性水平卜的MacKinnon临界值，故不能拒绝原假设，该序列是北平稳的。 做出LnC的散点图如下：对LnC序列进

31、行单位根检验，由于实际人均年消费支出对数序列序列具有截距，选择具有被 距的DF检验，得出的结果如下：Null Hypothesis: LNC has a unit rootExogenous: ConstantLag Length: 1 (Fixed)t-StatisticProb*Augmented Dickey-Fuller test statistic2.9904901.0000Test critical values:1 % level5% level10% level-3.610453-2 938987-2.607932MacKinnon (1996) one-sided p-val

32、ues.Augmented Dickey-Fuller Test EquationDependent Variable: D(LNC)Method. Least SquaresDate: 12/02/14 Time: 20 49Sample (adjusted): 1952 1990Included observations: 39 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.LNC(-1)0.0705020.0235752.9904900 0050D(LNC(-1)-0.0040480.180561-3.0224

33、210.9822c-0.3146440.118241-2.6610470 0116R-squared0.285902Mean dependent var0 054918Adjusted R-squared0.246230S.D.dependentvar0 068662S.E. of regression0.059612Akaike info criterion-2.7281 15Sum squared resid0.127929Schwarz criterion-2.600149Log likelihood56.19824Hannan-Quinn enter.-2.682202F-statis

34、tic7.206615Durbin-Watson stat1 998172Prob(r-statistic)0.002332从单位根检验可以看出，此时DW值为1.998172,与2很接近，而t统计量的值为2.990490,大于所有显著性水平卜的MacKinnon临界值，故不能拒绝原假设，该序列是北平稳的。(2)对LnY进行一阶差分后的单位根检验，选择具有截距的DF检验结果如卜.：Null Hypothesis D(LNY) has a unit rootExogenous: ConstantLag Length: 0 (Fixed)t-StatisticProb *Augmented Dick

35、ey-Fuller test statistic49391430.0002Test critical values:1 % level36104535% level-2.93898710% level-2.607932MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(LNY,2)Method: Least SquaresDate: 12/02/14 Time: 20.45Sample (adjusted): 1952 1990Included observ

36、ations: 39 after adjustmentsVanableCoefficientStd. Error t-StatisticProbD(LNY(-1)-0.7966690.161297-4.9391430 0000c0.0453720.0151932.9864880 0050R-squared0.397346Mean dependent var0 000283Adjusted R-squared0.381058S.D. dependentvar0.096397S.E. of regression0.075838Akaike info criterion-2.270502Sum sq

37、uared resid0.212805Schwarz critenon-2.185191Log likelihood46.27479Hannan-Quinn enter.-2.239893F-statistic24.39513Durbin-Watson stat2.145769Prob(F-statistic)0.000017从单位根检验可以在出，此时DW值为2.145769,与2很接近，而t统计量的值为4.939143, 小于99%显著性水平下的MacKinnon临界值，故拒绝原假设，认为一阶差分后的序列是平稳 的，即LnYl(1) o对LnC进行一阶差分后的单位根检验，选择具有截距的DF检

38、验结果如卜.：Null Hypothesis: D(LNC) has a unit rootExogenous: ConstantLag Length: 0 (Fixed)t-StatisticProb?Augmented Dickey-Fuller test statistic-4.2870410.0016Test critical values1 % level5% level10% level-3.610453-2.938987-2.607932eMacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test Equati

39、onDependent Variable: D(LNC,2)Method: Least SquaresDate: 12/02/14 Time: 20:52Sample (adjusted) 1952 1990Included observations: 39 after adjustmentsVariableCoefficientStd. Error t-StatisticProb.D(LNC(-1)-0.6688920.156026-4.2870410 0001c0 0370590.0134722.7507710 0091R-squared0 331873Mean dependent var

40、0 000981Adjusted R-squared0.313816S.D.dependentvar0.079313S.E. of regression0.065700Akaike info criterion-2.557520Sum squared resid0.159709Schwarz criterion-2 472210Log likelihood51 87165Hannan-Quinn enter-2 526912statistic18.37872Durbin-Watson stat2.284803Prob(F-statistic)0.000124从单位根检验可以看出，此时DW值为2

41、.284803,与2很接近，而t统计量的值为4287041, 小于99%显著性水平下的MacKinnon临界值，故拒绝原假设，认为一阶差分后的序列是平 稳的,即 LnCl (1) o由于LnY与LnC都是一阶单整序列，故可能存在协整关系，卜面通过检验残差序列的平稳 性来判断LnY与LnC是否存在协整关系接下来利用OLS回归方法对LnY与LnC进行回归估计，结果如下图所示：Dependent Variable: LNYMethod: Least SquaresDate: 12/02/14 Time. 23:43Sample: 1950 1990Included observations 41Va

42、nableCoefficientStd. Errort-StatisticProb.c0.2663070.0640834.1556530 0002LNC1.0563310.01210537.261900.0000R-squared0.994904Mean dependent var5.826358Adjusted R-squared0.994774S.D. dependent var0.606026S.E. of regression0 043811Akaike info critenon-3 370294Sum squared residLog likelihood F-stat)stic

43、Prob(F-statistJC)0.074858 Schwarz cntenon71.09103 Hannan-Quinn enter.7614.640 Durbin-Watson stat0 000000-3 286705-3.3398561 435780得到的回归模型为_I 函=0.266307+1.056331InCt所以残差序列为生二 lnK-0.266307+1.056331InG做出残差的散点图对残差序列进行单位根检验，由于残差序列均值为0,则选择其没有截距没有趋势，滞后长度为1的ADF检验，得出的结果如下：Null Hypothesis: E has a unit rootEx

44、ogenous: NoneLag Length: 1 (Fixed)t-StatisticProb?Augmented Dickey-Fuller test statistic40985830.0001Test critical values:1 % level-2.6256065% level-1.94960910% level-1.611593MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationD即endent Variable D(E)Method: Least SquaresDate: 12/08/14 Time: 12 33Sample (adjusted): 1952 1990Inc