實驗三-金融數(shù)據(jù)的平穩(wěn)性檢驗實驗指導(dǎo)

1、 一、實驗?zāi)康模豪斫饨?jīng)濟時間序列存在的不平穩(wěn)性，掌握 ADF檢驗平穩(wěn)性的方法。認識不平穩(wěn)的序列容易導(dǎo)致偽回歸問題，掌握為解決偽回歸問題引出的協(xié)整檢驗，協(xié)整的概念和具體的協(xié)整檢驗過程。協(xié)整描述了變量之間的長期關(guān)系，為了進一步研究變量之間的短期均衡是否存在，掌握誤差糾正模型方法。理解變量之間的因果關(guān)系的計量意義，掌握格蘭杰因果檢驗方法。二、基本概念：如果一個隨機過程的均值和方差在時間過程上都是常數(shù)，并且在任何兩時期的協(xié)方差值僅依賴于該兩時期間的距離或滯后，而不依賴于計算這個協(xié)方差的實際時間，就稱它為平穩(wěn)的。強調(diào)平穩(wěn)性是因為將一個隨機游走變量（即非平穩(wěn)數(shù)據(jù)）對另一個隨機游走變量進行回歸可能導(dǎo)致荒謬的

2、結(jié)果，傳統(tǒng)的顯著性檢驗將告知我們變量之間的關(guān)系是不存在的。這種情Spurious Regression有時雖然兩個變量都是隨機游走的，但它們的某個線形組合卻可能是平穩(wěn)的，在這種情況下，我們稱這兩個變量是協(xié)整的。因果檢驗用于確定一個變量的變化是否為另一個變量變化的原因。三、實驗內(nèi)容及要求：用 Eviews 來分析上海證券市場 A股成份指數(shù)（簡記 SHA）和深圳證券市場 A股成份指數(shù)（簡記 SZA）之間的關(guān)系。內(nèi)容包括：1.對數(shù)據(jù)進行平穩(wěn)性檢驗2.協(xié)整檢驗3.因果檢驗4.誤差糾正機制 ECM要求：在認真理解本章內(nèi)容的基礎(chǔ)上，通過實驗掌握 ADF檢驗平穩(wěn)性的方法，具體的協(xié)整檢驗過程，掌握格蘭杰因果檢

3、驗方法，以及誤差糾正模型方法。四、實驗指導(dǎo)：1、對數(shù)據(jù)進行平穩(wěn)性檢驗：首先導(dǎo)入數(shù)據(jù)，將上海證券市場A股成份指數(shù)記為 SHA，深圳證券市場A股成份指數(shù)記為 SZA（若已有 wf1 在 workfile中按住 ctrl 選擇要檢驗的二變量，右擊，選擇 openas group。則此時可在彈出的窗口中對選中的變量進行檢驗。檢驗方法有： View”“graph”“ 31 所示。畫直方圖：在 workfile 中按住選擇要檢驗的變量，右擊，選擇 open，或雙擊選中的view”“descriptive statistic”“histogram and stats 統(tǒng)計量，其越趨向于 0，則圖越符合正態(tài)分

4、布，也就說明數(shù)據(jù)越平穩(wěn)。如圖 32和 33 所示。用 ADFviewunit root testquick“series statistic”“unit root test ok，如圖 34 和 36 所示。圖 31 SHA和 SZA 原始數(shù)值線性圖圖 32 SHA原始數(shù)值直方圖圖 33 SZA原始數(shù)值直方圖圖 34 單位根檢驗對話框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)圖 35 SHA數(shù)值的 ADF檢驗結(jié)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)圖 36 SZA數(shù)值的 ADF檢驗結(jié)果粗略觀查數(shù)據(jù)并不平

11、穩(wěn)。此時應(yīng)對數(shù)據(jù)取對數(shù)（取對數(shù)的好處在于：即可以將間距很大的數(shù)據(jù)轉(zhuǎn)換為間距較小的數(shù)據(jù)，也便于后面的取差分），再對新變量進行平穩(wěn)性檢驗。點擊Eviews quick”“generate series”鍵入logsha=log(sha)，同樣的方法得到。此時，logsha 和 logsza為新變量，對其進行平穩(wěn)性檢驗方法如上，發(fā)現(xiàn)也是不平穩(wěn)的。圖 37 SHA和 SZA 對數(shù)值線性圖用 ADF方法檢驗 logsha 和 logsza的平穩(wěn)性。通過比較檢驗值和不同顯著性下的關(guān)鍵值來得出結(jié)論。如下圖（前者是對SHA檢驗結(jié)果，后者是對SZA 檢驗結(jié)果）中所示，檢驗值小于關(guān)鍵值，則得出數(shù)據(jù)不平穩(wěn)，反之平穩(wěn)

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)圖 38 SHA對數(shù)值的 ADF檢驗結(jié)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)圖 39 SZA對數(shù)值的 ADF檢驗結(jié)果2、協(xié)整檢驗：quickestimate equationlogsha c logsza得到結(jié)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)圖 310 logsza對 logsha 的最小二乘法回歸接著在窗口中點擊“procsmake residual series resid01 進行提取和保存；然后對殘差進行 ADFresid01 是平穩(wěn)的。所以 logsha 同 logsza有協(xié)整關(guān)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)圖 311 殘差resid01 的 ADF檢驗結(jié)果接下來以同樣的方法協(xié)整 logsza c logsha,得到殘差resid02，經(jīng)過檢驗也是平穩(wěn)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)圖 312 殘差resid02的 ADF檢驗結(jié)果3、因果檢驗：在 workfile中同時選中“l(fā)ogsha”和“open”“as group彈出的窗口中點擊“view”“granger causality”并選擇滯后階數(shù)（此處我

28、們根據(jù)以往的實證檢驗結(jié)果選擇滯后值為 5 ok，結(jié)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圖 313 格蘭杰因果檢驗結(jié)果先看 F 檢驗值，如前所述，若 F 值大，則拒絕假設(shè)。在本例中即 logsza是 logsha 變化的原因；而 logsha 不影響 。同樣的結(jié)論也可以從 Probability中得到。4、誤差糾正機制 ECM（error correction mechanism）即使兩個變量之間有長期均衡關(guān)系，但在短期內(nèi)也會出現(xiàn)失衡（例如收突發(fā)事件的影 ECM來對這種短期失衡加以糾正。sha c sza”resid03quick“estimate d(sha) c d(sza) resid03(-1)Resid03(-1)中的(-1)指的是滯后一階，結(jié)果如下：Dependent Vari