实验三-金融数据的平稳性检验实验指导

1、 一、实验目的：理解经济时间序列存在的不平稳性，掌握 ADF检验平稳性的方法。认识不平稳的序列容易导致伪回归问题，掌握为解决伪回归问题引出的协整检验，协整的概念和具体的协整检验过程。协整描述了变量之间的长期关系，为了进一步研究变量之间的短期均衡是否存在，掌握误差纠正模型方法。理解变量之间的因果关系的计量意义，掌握格兰杰因果检验方法。二、基本概念：如果一个随机过程的均值和方差在时间过程上都是常数，并且在任何两时期的协方差值仅依赖于该两时期间的距离或滞后，而不依赖于计算这个协方差的实际时间，就称它为平稳的。强调平稳性是因为将一个随机游走变量（即非平稳数据）对另一个随机游走变量进行回归可能导致荒谬的

2、结果，传统的显著性检验将告知我们变量之间的关系是不存在的。这种情Spurious Regression有时虽然两个变量都是随机游走的，但它们的某个线形组合却可能是平稳的，在这种情况下，我们称这两个变量是协整的。因果检验用于确定一个变量的变化是否为另一个变量变化的原因。三、实验内容及要求：用 Eviews 来分析上海证券市场 A股成份指数（简记 SHA）和深圳证券市场 A股成份指数（简记 SZA）之间的关系。内容包括：1.对数据进行平稳性检验2.协整检验3.因果检验4.误差纠正机制 ECM要求：在认真理解本章内容的基础上，通过实验掌握 ADF检验平稳性的方法，具体的协整检验过程，掌握格兰杰因果检

3、验方法，以及误差纠正模型方法。四、实验指导：1、对数据进行平稳性检验：首先导入数据，将上海证券市场A股成份指数记为 SHA，深圳证券市场A股成份指数记为 SZA（若已有 wf1 在 workfile中按住 ctrl 选择要检验的二变量，右击，选择 openas group。则此时可在弹出的窗口中对选中的变量进行检验。检验方法有： View”“graph”“ 31 所示。画直方图：在 workfile 中按住选择要检验的变量，右击，选择 open，或双击选中的view”“descriptive statistic”“histogram and stats 统计量，其越趋向于 0，则图越符合正态分

4、布，也就说明数据越平稳。如图 32和 33 所示。用 ADFviewunit root testquick“series statistic”“unit root test ok，如图 34 和 36 所示。图 31 SHA和 SZA 原始数值线性图图 32 SHA原始数值直方图图 33 SZA原始数值直方图图 34 单位根检验对话框ADF Test Statistic-1.8248061%5%Critical Value*Critical Value-3.4369-2.8636-2.567910% Critical Value*MacKinnon critical values for re

5、jection of hypothesis of a unit root.Augmented Dickey-Fuller Test EquationDependent Variable: D(S HA)Method: Least SquaresDate: 10/25/05Time: 00:50Sample(adjusted): 1/08/1993 12/31/1999Included observations: 1821 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb.SHA(-1)D(SHA(-1)D

6、(SHA(-2)D(SHA(-3)D(SHA(-4)C-0.003575-0.038736-0.0107970.1111270.0623803.9430770.0019590.0234270.0233080.0232870.0233992.121673-1.824806-1.653464-0.4632174.7721492.6659011.8584760.06820.09840.64330.00000.00770.0633R-squared0.0184470.01574327.655381388148.-8626.2752.001095Mean dependent var 0.295316Ad

7、justed R-squaredS.E. of regressionSum squared residLog likelihoodS.D. dependent varAkaike info criterionSchwarz criterionF-statistic27.875689.4808079.4989526.8222570.000003Durbin-Watson statProb(F-statistic)图 35 SHA数值的 ADF检验结果ADF Test Statistic-1.3868971%5%Critical Value* -3.4369Critical Value-2.863

8、6-2.567910% Critical Value*MacKinnon critical values for rejection of hypothesis of a unit root.Augmented Dickey-Fuller Test EquationDependent Variable: D(SZA)Method: Least SquaresDate: 02/14/07Time: 09:28Sample(adjusted): 1/08/1993 12/31/1999Included observations: 1821 after adjusting endpointsVari

9、ableCoefficientStd. Error t-StatisticProb.SZA(-1)D(SZA(-1)D(SZA(-2)D(SZA(-3)D(SZA(-4)C-0.001999-0.0286380.0296640.0846500.0814280.6677860.001441 -1.3868970.023396 -1.2240560.023325 1.2717550.023327 3.6288170.023390 3.4813800.466362 1.4319050.16560.22110.20360.00030.00050.1523R-squared0.0154050.01269

10、37.789199110119.0-6318.9181.998663Mean dependent var 0.087348S.D. dependent var 7.839108Akaike info criterion 6.946643Adjusted R-squaredS.E. of regressionSum squared residLog likelihoodSchwarz criterionF-statistic6.9647885.6795240.000033Durbin-Watson statProb(F-statistic)图 36 SZA数值的 ADF检验结果粗略观查数据并不平

11、稳。此时应对数据取对数（取对数的好处在于：即可以将间距很大的数据转换为间距较小的数据，也便于后面的取差分），再对新变量进行平稳性检验。点击Eviews quick”“generate series”键入logsha=log(sha)，同样的方法得到。此时，logsha 和 logsza为新变量，对其进行平稳性检验方法如上，发现也是不平稳的。图 37 SHA和 SZA 对数值线性图用 ADF方法检验 logsha 和 logsza的平稳性。通过比较检验值和不同显著性下的关键值来得出结论。如下图（前者是对SHA检验结果，后者是对SZA 检验结果）中所示，检验值小于关键值，则得出数据不平稳，反之平稳

12、。ADF Test Statistic-1.7955261%5%Critical Value*Critical Value-3.4369-2.8636-2.567910% Critical Value*MacKinnon critical values for rejection of hypothesis of a unit root.Augmented Dickey-Fuller Test EquationDependent Variable: D(LOGSHA)Method: Least SquaresDate: 02/14/07Time: 09:42Sample(adjusted):

13、1/08/1993 12/31/1999Included observations: 1821 after adjusting endpointsVariableCoefficient-0.003583Std. Error t-Statistic0.001995 -1.795526Prob.LOGSHA(-1)0.0727D(LOGSHA(-1)D(LOGSHA(-2)D(LOGSHA(-3)D(LOGSHA(-4)C-0.0347250.0205250.0652360.0343230.0248920.023459 -1.4802610.023427 0.8761280.023404 2.78

14、73540.023421 1.4654760.013751 1.8101560.13900.38110.00540.14300.0704R-squared0.0081230.0053910.0289231.5183133871.1402.001003Mean dependent varS.D. dependent varAkaike info criterionSchwarz criterionF-statistic0.0002540.029001-4.245075-4.2269292.9728450.011179Adjusted R-squaredS.E. of regressionSum

15、squared residLog likelihoodDurbin-Watson statProb(F-statistic)图 38 SHA对数值的 ADF检验结果ADF Test Statistic-1.2361191%5%Critical Value*Critical Value-3.4369-2.8636-2.567910% Critical Value*MacKinnon critical values for rejection of hypothesis of a unit root.Augmented Dickey-Fuller Test EquationDependent Va

16、riable: D(LOGSZA)Method: Least SquaresDate: 02/14/07Time: 09:43Sample(adjusted): 1/08/1993 12/31/1999Included observations: 1821 after adjusting endpointsVariableCoefficientStd. Error t-StatisticProb.LOGSZA(-1)D(LOGSZA(-1)D(LOGSZA(-2)D(LOGSZA(-3)D(LOGSZA(-4)C-0.001645-0.0106390.0436710.0332840.07828

17、40.0094040.001331 -1.2361190.023402 -0.4546000.023391 1.8669820.023393 1.4228250.023392 3.3466590.007463 1.2600370.21660.64950.06210.15500.00080.2078R-squared0.0099840.0072570.0278971.4124683936.9342.001713Mean dependent varS.D. dependent varAkaike info criterionSchwarz criterionF-statistic0.0002520

18、.027998-4.317335-4.2991903.6607820.002675Adjusted R-squaredS.E. of regressionSum squared residLog likelihoodDurbin-Watson statProb(F-statistic)图 39 SZA对数值的 ADF检验结果2、协整检验：quickestimate equationlogsha c logsza得到结果如下：Dependent Variable: LOGSHAMethod: Least SquaresDate: 02/14/07Time: 09:52Sample: 1/01/1

19、993 12/31/1999Included observations: 1826VariableCoefficientStd. Errort-StatisticProb.C3.1852650.6618510.0269850.004811118.0392137.57330.00000.0000LOGSZAR-squared0.9120980.9120500.10110718.646001594.4400.041307Mean dependent varS.D. dependent varAkaike info criterionSchwarz criterionF-statistic6.883

20、3580.340928-1.744184-1.73814918926.430.000000Adjusted R-squaredS.E. of regressionSum squared residLog likelihoodDurbin-Watson statProb(F-statistic)图 310 logsza对 logsha 的最小二乘法回归接着在窗口中点击“procsmake residual series resid01 进行提取和保存；然后对残差进行 ADFresid01 是平稳的。所以 logsha 同 logsza有协整关系。ADF Test Statistic -4.132

21、3161%5%Critical Value*Critical Value-3.4369-2.8636-2.567910% Critical Value*MacKinnon critical values for rejection of hypothesis of a unit root.Augmented Dickey-Fuller Test EquationDependent Variable: D(RESID01)Method: Least SquaresDate: 02/14/07Time: 10:01Sample(adjusted): 1/08/1993 12/31/1999Incl

22、uded observations: 1821 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb.RESID01(-1)D(RESID01(-1)D(RESID01(-2)D(RESID01(-3)D(RESID01(-4)C-0.019808-0.089306-0.0201150.0643040.0220899.14E-050.0047930.0234970.0235630.0234970.0233960.000476-4.132316-3.800810-0.8536912.7367350.944140

23、0.1921990.00000.00010.39340.00630.34520.8476R-squared0.0230200.0203290.020303Mean dependent varS.D. dependent varAkaike info criterion8.71E-050.020512-4.952841Adjusted R-squaredS.E. of regressionSum squared residLog likelihood0.7481394515.5611.996742Schwarz criterionF-statistic-4.9346958.5531920.000

24、000Durbin-Watson statProb(F-statistic)图 311 残差resid01 的 ADF检验结果接下来以同样的方法协整 logsza c logsha,得到残差resid02，经过检验也是平稳的。ADF Test Statistic-3.9001001%5%Critical Value*Critical Value-3.4369-2.8636-2.567910% Critical Value*MacKinnon critical values for rejection of hypothesis of a unit root.Augmented Dickey-F

25、uller Test EquationDependent Variable: D(RESID02)Method: Least SquaresDate: 02/14/07Time: 10:03Sample(adjusted): 1/08/1993 12/31/1999Included observations: 1821 after adjusting endpointsVariableCoefficient Std. Errort-StatisticProb.RESID02(-1)D(RESID02(-1)D(RESID02(-2)D(RESID02(-3)D(RESID02(-4)C-0.0

26、17724 0.004544-0.095416 0.023495-0.024582 0.0235770.059774 0.0235110.022353 0.023395-0.000105 0.000652-3.900100-4.061081-1.0426212.5423560.955429-0.1605970.00010.00010.29730.01110.33950.8724R-squared0.0228320.0201400.0278411.4068453940.5661.996185Mean dependent var -9.79E-05Adjusted R-squaredS.E. of

27、 regressionSum squared residLog likelihoodS.D. dependent varAkaike info criterionSchwarz criterionF-statistic0.028126-4.321324-4.3031798.4817650.000000Durbin-Watson statProb(F-statistic)图 312 残差resid02的 ADF检验结果3、因果检验：在 workfile中同时选中“logsha”和“open”“as group弹出的窗口中点击“view”“granger causality”并选择滞后阶数（此处我

28、们根据以往的实证检验结果选择滞后值为 5 ok，结果如下：Pairwise Granger Causality TestsDate: 02/14/07Time: 10:10Sample: 1/01/1993 12/31/1999Lags: 1Null Hypothesis:Obs F-Statistic ProbabilityLOGSZA does not Granger Cause LOGSHA 1825 12.83280.000350.22917LOGSHA does not Granger Cause LOGSZAPairwise Granger Causality Tests1.447

29、01Date: 02/14/07Time: 10:11Sample: 1/01/1993 12/31/1999Lags: 2Null Hypothesis:Obs F-Statistic ProbabilityLOGSZA does not Granger Cause LOGSHA 1824 8.314560.000250.40150LOGSHA does not Granger Cause LOGSZA0.91301Pairwise Granger Causality TestsDate: 02/14/07Time: 10:11Sample: 1/01/1993 12/31/1999Lags

30、: 3Null Hypothesis:Obs F-Statistic ProbabilityLOGSZA does not Granger Cause LOGSHA 1823 5.838920.000570.39435LOGSHA does not Granger Cause LOGSZAPairwise Granger Causality Tests0.99468Date: 02/14/07Time: 10:12Sample: 1/01/1993 12/31/1999Lags: 4Null Hypothesis:Obs F-Statistic ProbabilityLOGSZA does n

31、ot Granger Cause LOGSHA 1822 4.392650.001550.52217LOGSHA does not Granger Cause LOGSZAPairwise Granger Causality Tests0.80455Date: 02/14/07Time: 10:09Sample: 1/01/1993 12/31/1999Lags: 5Null Hypothesis:Obs F-Statistic ProbabilityLOGSZA does not Granger Cause LOGSHA 1821 3.601840.003030.62045LOGSHA do

32、es not Granger Cause LOGSZA0.70399图 313 格兰杰因果检验结果先看 F 检验值，如前所述，若 F 值大，则拒绝假设。在本例中即 logsza是 logsha 变化的原因；而 logsha 不影响 。同样的结论也可以从 Probability中得到。4、误差纠正机制 ECM（error correction mechanism）即使两个变量之间有长期均衡关系，但在短期内也会出现失衡（例如收突发事件的影 ECM来对这种短期失衡加以纠正。sha c sza”resid03quick“estimate d(sha) c d(sza) resid03(-1)Resid03(-1)中的(-1)指的是滞后一阶，结果如下：Dependent Vari