1、协整检验步骤实验三 金融数据的平稳性检验实验指导一、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
2、）对另一个随机游走变量进行回归可能导致荒谬的结果，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。这种情况就称为“伪回归”（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
3、验平稳性的方法，具体的协整检验过程，掌握格兰杰因果检验方法，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文件则直接打开该文件）。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：1画折线图：“View”“graph”“line”，如图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，或双击选中的变量，“view”“descriptive statisti
4、c”“histogram and stats”；注意到图中的J.B.统计量，其越趋向于0，则图越符合正态分布，也就说明数据越平稳。如图32和33所示。用ADF检验：方法一：“view”“unit root test”；方法二：点击菜单中的“quick”“series statistic”“unit root test”；分析原则即比较值的大小以及经验法则。点击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-1.824806 1% Critical Value*-3
5、.4369 5% Critical Value-2.8636 10% Critical Value-2.5679*MacKinnon critical values for rejection of hypothesis of a unit root.Augmented Dickey-Fuller Test EquationDependent Variable: D(SHA)Method: Least SquaresDate: 10/25/05 Time: 00:50Sample(adjusted): 1/08/1993 12/31/1999Included observations: 182
6、1 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. SHA(-1)-0.0035750.001959-1.8248060.0682D(SHA(-1)-0.0387360.023427-1.6534640.0984D(SHA(-2)-0.0107970.023308-0.4632170.6433D(SHA(-3)0.1111270.0232874.7721490.0000D(SHA(-4)0.0623800.0233992.6659010.0077C3.9430772.1216731.8584760.0
7、633R-squared0.018447 Mean dependent var0.295316Adjusted R-squared0.015743 S.D. dependent var27.87568S.E. of regression27.65538 Akaike info criterion9.480807Sum squared resid1388148. Schwarz criterion9.498952Log likelihood-8626.275 F-statistic6.822257Durbin-Watson stat2.001095 Prob(F-statistic)0.0000
8、03 图35 SHA数值的ADF检验结果ADF Test Statistic-1.386897 1% Critical Value*-3.4369 5% Critical Value-2.8636 10% Critical Value-2.5679*MacKinnon critical values for rejection of hypothesis of a unit root.Augmented Dickey-Fuller Test EquationDependent Variable: D(SZA)Method: Least SquaresDate: 02/14/07 Time: 0
9、9:28Sample(adjusted): 1/08/1993 12/31/1999Included observations: 1821 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. SZA(-1)-0.0019990.001441-1.3868970.1656D(SZA(-1)-0.0286380.023396-1.2240560.2211D(SZA(-2)0.0296640.0233251.2717550.2036D(SZA(-3)0.0846500.0233273.6288170.0003D
10、(SZA(-4)0.0814280.0233903.4813800.0005C0.6677860.4663621.4319050.1523R-squared0.015405 Mean dependent var0.087348Adjusted R-squared0.012693 S.D. dependent var7.839108S.E. of regression7.789199 Akaike info criterion6.946643Sum squared resid110119.0 Schwarz criterion6.964788Log likelihood-6318.918 F-s
11、tatistic5.679524Durbin-Watson stat1.998663 Prob(F-statistic)0.000033 图36 SZA数值的ADF检验结果 粗略观查数据并不平稳。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中的“quick”“generate series”键入logsha=log(sha)，同样的方法得到logsza。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lo
12、gsha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。ADF Test Statistic-1.795526 1% Critical Value*-3.4369 5% Critical Value-2.8636 10% Critical Value-2.5679*MacKinnon critical values for rejection of hypothesis of a unit root.Augmented Dickey-Fuller Test Eq
13、uationDependent Variable: D(LOGSHA)Method: Least SquaresDate: 02/14/07 Time: 09:42Sample(adjusted): 1/08/1993 12/31/1999Included observations: 1821 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. LOGSHA(-1)-0.0035830.001995-1.7955260.0727D(LOGSHA(-1)-0.0347250.023459-1.4802610
14、.1390D(LOGSHA(-2)0.0205250.0234270.8761280.3811D(LOGSHA(-3)0.0652360.0234042.7873540.0054D(LOGSHA(-4)0.0343230.0234211.4654760.1430C0.0248920.0137511.8101560.0704R-squared0.008123 Mean dependent var0.000254Adjusted R-squared0.005391 S.D. dependent var0.029001S.E. of regression0.028923 Akaike info cr
15、iterion-4.245075Sum squared resid1.518313 Schwarz criterion-4.226929Log likelihood3871.140 F-statistic2.972845Durbin-Watson stat2.001003 Prob(F-statistic)0.011179图38 SHA对数值的ADF检验结果ADF Test Statistic-1.236119 1% Critical Value*-3.4369 5% Critical Value-2.8636 10% Critical Value-2.5679*MacKinnon criti
16、cal values for rejection of hypothesis of a unit root.Augmented Dickey-Fuller Test EquationDependent Variable: D(LOGSZA)Method: Least SquaresDate: 02/14/07 Time: 09:43Sample(adjusted): 1/08/1993 12/31/1999Included observations: 1821 after adjusting endpointsVariableCoefficientStd. Errort-StatisticPr
17、ob. LOGSZA(-1)-0.0016450.001331-1.2361190.2166D(LOGSZA(-1)-0.0106390.023402-0.4546000.6495D(LOGSZA(-2)0.0436710.0233911.8669820.0621D(LOGSZA(-3)0.0332840.0233931.4228250.1550D(LOGSZA(-4)0.0782840.0233923.3466590.0008C0.0094040.0074631.2600370.2078R-squared0.009984 Mean dependent var0.000252Adjusted
18、R-squared0.007257 S.D. dependent var0.027998S.E. of regression0.027897 Akaike info criterion-4.317335Sum squared resid1.412468 Schwarz criterion-4.299190Log likelihood3936.934 F-statistic3.660782Durbin-Watson stat2.001713 Prob(F-statistic)0.002675 图39 SZA对数值的ADF检验结果2、协整检验：首先要提取残差：点击菜单中的“quick”“estim
19、ate equation”键入“logsha c logsza”，得到结果如下：Dependent Variable: LOGSHAMethod: Least SquaresDate: 02/14/07 Time: 09:52Sample: 1/01/1993 12/31/1999Included observations: 1826VariableCoefficientStd. Errort-StatisticProb. C3.1852650.026985118.03920.0000LOGSZA0.6618510.004811137.57330.0000R-squared0.912098 M
20、ean dependent var6.883358Adjusted R-squared0.912050 S.D. dependent var0.340928S.E. of regression0.101107 Akaike info criterion-1.744184Sum squared resid18.64600 Schwarz criterion-1.738149Log likelihood1594.440 F-statistic18926.43Durbin-Watson stat0.041307 Prob(F-statistic)0.000000图310 logsza对logsha的
21、最小二乘法回归接着在窗口中点击“procs”“make residual series”来对残差resid01进行提取和保存；然后对残差进行ADF检验（方法同上），得到结果如下图。你会发现数据通过了检验，残差resid01是平稳的。所以logsha同logsza有协整关系。ADF Test Statistic-4.132316 1% Critical Value*-3.4369 5% Critical Value-2.8636 10% Critical Value-2.5679*MacKinnon critical values for rejection of hypothesis of a
22、 unit root.Augmented Dickey-Fuller Test EquationDependent Variable: D(RESID01)Method: Least SquaresDate: 02/14/07 Time: 10:01Sample(adjusted): 1/08/1993 12/31/1999Included observations: 1821 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. RESID01(-1)-0.0198080.004793-4.1323160
23、.0000D(RESID01(-1)-0.0893060.023497-3.8008100.0001D(RESID01(-2)-0.0201150.023563-0.8536910.3934D(RESID01(-3)0.0643040.0234972.7367350.0063D(RESID01(-4)0.0220890.0233960.9441400.3452C9.14E-050.0004760.1921990.8476R-squared0.023020 Mean dependent var8.71E-05Adjusted R-squared0.020329 S.D. dependent va
24、r0.020512S.E. of regression0.020303 Akaike info criterion-4.952841Sum squared resid0.748139 Schwarz criterion-4.934695Log likelihood4515.561 F-statistic8.553192Durbin-Watson stat1.996742 Prob(F-statistic)0.000000 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 Statist
25、ic-3.900100 1% Critical Value*-3.4369 5% Critical Value-2.8636 10% Critical Value-2.5679*MacKinnon critical values for rejection of hypothesis of a unit root.Augmented Dickey-Fuller Test EquationDependent Variable: D(RESID02)Method: Least SquaresDate: 02/14/07 Time: 10:03Sample(adjusted): 1/08/1993
26、12/31/1999Included observations: 1821 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. RESID02(-1)-0.0177240.004544-3.9001000.0001D(RESID02(-1)-0.0954160.023495-4.0610810.0001D(RESID02(-2)-0.0245820.023577-1.0426210.2973D(RESID02(-3)0.0597740.0235112.5423560.0111D(RESID02(-4)0.
27、0223530.0233950.9554290.3395C-0.0001050.000652-0.1605970.8724R-squared0.022832 Mean dependent var-9.79E-05Adjusted R-squared0.020140 S.D. dependent var0.028126S.E. of regression0.027841 Akaike info criterion-4.321324Sum squared resid1.406845 Schwarz criterion-4.303179Log likelihood3940.566 F-statist
28、ic8.481765Durbin-Watson stat1.996185 Prob(F-statistic)0.000000 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“logsza”，右击，选择“open”“as group”，在弹出的窗口中点击“view”“granger causality”并选择滞后阶数（此处我们根据以往的实证检验结果选择滞后值为5），点ok，结果如下：Pairwise Granger Causality TestsDate: 02/14/07 Time: 10:10Sample: 1/01/1993 12/31/1999Lags: 1 Null Hypothesis:ObsF-StatisticProbability LOGSZA does not Granger Cause LOGSHA1825
