金融計(jì)量學(xué)-因果檢驗(yàn)

1、實(shí)驗(yàn)四 金融數(shù)據(jù)的平穩(wěn)性檢驗(yàn)實(shí)驗(yàn)一、實(shí)驗(yàn)?zāi)康睦斫饨?jīng)濟(jì)時(shí)間序列存在的不平穩(wěn)性，掌握ADF檢驗(yàn)平穩(wěn)性的方法。認(rèn)識(shí)不平穩(wěn)的序列 容易導(dǎo)致偽回歸問(wèn)題，掌握為解決偽回歸問(wèn)題引出的協(xié)整檢驗(yàn)，協(xié)整的概念和具體的協(xié)整檢 驗(yàn)過(guò)程。協(xié)整描述了變量之間的長(zhǎng)期關(guān)系，為了進(jìn)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(jì)量意義，掌握格蘭杰因果檢驗(yàn)方法。二、基本概念如果一個(gè)隨機(jī)過(guò)程的均值和方差在時(shí)間過(guò)程上都是常數(shù)，并且在任何兩時(shí)期的協(xié)方差值 僅依賴于該兩時(shí)期間的距離或滯后，而不依賴于計(jì)算這個(gè)協(xié)方差的實(shí)際時(shí)間，就稱它為平穩(wěn) 的。強(qiáng)調(diào)平穩(wěn)性是因?yàn)閷⒁粋€(gè)隨機(jī)游走變量（即非平穩(wěn)數(shù)據(jù)）對(duì)另一個(gè)

2、隨機(jī)游走變量進(jìn)行回 歸可能導(dǎo)致荒謬的結(jié)果，傳統(tǒng)的顯著性檢驗(yàn)將告知我們變量之間的關(guān)系是不存在的。這種情 況就稱為“偽回歸”（Spurious Regression）。有時(shí)雖然兩個(gè)變量都是隨機(jī)游走的，但它們的某個(gè)線形組合卻可能是平穩(wěn)的，在這種情 況下，我們稱這兩個(gè)變量是協(xié)整的。因果檢驗(yàn)用于確定一個(gè)變量的變化是否為另一個(gè)變量變化的原因。三、實(shí)驗(yàn)內(nèi)容用Eviews來(lái)分析A股不同行業(yè)的兩只股票，對(duì)數(shù)據(jù)進(jìn)行平穩(wěn)性檢驗(yàn)。四、實(shí)驗(yàn)指導(dǎo)：1、對(duì)數(shù)據(jù)進(jìn)行平穩(wěn)性檢驗(yàn)：首先導(dǎo)入數(shù)據(jù)，將股票SHA和SZA輸入（若已有wf1文件則直接打開(kāi)該文件）。在workfile中按住ctrl選擇要檢驗(yàn)的二變量，右擊，選擇openas

3、 group。則此時(shí)可在 彈出的窗口中對(duì)選中的變量進(jìn)行檢驗(yàn)。檢驗(yàn)方法有：畫(huà)折線圖：“View”一graph”一Tine”，如圖1所示。畫(huà)直方圖：在workfile中按住選擇要檢驗(yàn)的變量，右擊，選擇open，或雙擊選中的 變量，“view” “descriptive statistic”一histogram and stats”；注意到圖中的J.B.統(tǒng)計(jì)量， 其越趨向于0，則圖越符合正態(tài)分布，也就說(shuō)明數(shù)據(jù)越平穩(wěn)。如圖2和3所示。用ADF檢驗(yàn)：方法一：“view”一 unit root test”；方法二：點(diǎn)擊菜單中的“quick”一 “ series statistic” 一 “ unit ro

4、ot test ”；分析原則即比較值的大小以及經(jīng)驗(yàn)法則。EievsISeries: SHA Torkfihe: UNTIJLED1 FileObj sets Vi ew Procs 里uiek Oti ore Window HelpVi ew I Procs I Llbj ectsEditPrintiNameiFreezeI Sample IGenrI Sheet I Stats IIdentI Line I Bar I200 h150-100-Series: SHASample W1/1993 12/31/1999Observations 1826MeanMedianSHA原始數(shù)值.直方圖m

5、Minimum1031.629 1006.362 1842.610328.8480Torkfile: UKTITLEDI I File Edi t Obj ects Vi ew Procs Quick Oji+iotle Wiridow HelpVi e,i*i, I Procs I Obj ectsFrint N：=iirie Freeze I SipleJ Gem- Sheet I Stats I IilerLt 1 Litlh E：=lt的數(shù)Eview時(shí)，300250200a阻據(jù)fS中的ogShaSeries: SZASample 1AJ1 /1993 12/31 /1999Observ

6、ations 1826并不平穩(wěn)。此時(shí)孫的數(shù)據(jù)，一企贏圖3 SZA原始數(shù)值直方|圖297.9938Median319.4905Maximum561.5640對(duì)數(shù)的好處在于日；即可以 再對(duì)新變量進(jìn)行平穩(wěn)性度據(jù)取對(duì)數(shù)(取 后面的取差分)， s” 鍵入 logsha= 穩(wěn)性檢驗(yàn)方og聊a),同樣的方法得到i(法如上，r發(fā)現(xiàn)也是不平穩(wěn)的。PrnhAhilrtwIllllll間距很大 驗(yàn)。點(diǎn)擊 gsza。此匕rlogsna 和 logsza的關(guān)鍵值來(lái)得出結(jié)論。如圖對(duì)SZA檢驗(yàn)結(jié)果中所示，檢驗(yàn)值小于關(guān)鍵值，則得出數(shù)據(jù)不平穩(wěn)，反之平穩(wěn)。ADF Test Statistic -1.2361191% Critic

7、al Value* -3.43695% Critical Value-2.863610% Critical Value-2.5679*MacKinnon critical 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 obse

8、rvations: 1821 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb.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.

9、0094040.0074631.2600370.2078R-squared0.009984Mean dependent var0.000252Adjusted R-squared0.007257S.D. dependent var0.027998S.E. of regression0.027897Akaike info criterion-4.317335Sum squared resid1.412468Schwarz criterion-4.299190Log likelihood3936.934F-statistic3.660782Durbin-Watson stat _2.001713_

10、Prob(F-statistic)_0.002675圖5SZA對(duì)數(shù)值的ADF檢驗(yàn)結(jié)果卻 E.lm 1 1Q0DOb&efvatiDns 10SDMe-an3135.458Median3158.597MaDcimum51 6.350Minimum2003.487Std. Dar.559.B19D0.376135Kurtrsis4.Q&4S75Jarqu-BE-ra1 37.BS4Pra-babilityo.aocooo腿?。篠2ASample1 1000Obiwsti&ns 10DDMean10633.5-9M-edisn1C5B4.&SM-aximLm1-809S.27M in imum715

11、1.1S0Std. Dev.1-S57.77SShewn bss0.S 07796KurtMis5.416745Jarq u e-B era352 1&B-Probs bi lityO.ODDOOOVa liableCoefficientStd. ErrorProb.SHA(-1)-0.0044-04-0 003064-1.47 4640.15090.1083360.03U&43.4443150.0006D(SHA(-2)-0.0867190.031635-2.7409540.0062D(SHA(-3)0.0206110.0316230.8&17B10.5147D(SHA(-4)0.15580

12、.031 4-664 9523890.0000C12.997599.7661831.3308770.1B35R-squared0.045S71Mean dependentvar-1.030000Adjusted R-squared0.0410+7SLD. dependentvar54.766B3S.E. of regression53.63103Maike info criterion10.30814Sum squared reid234+643.Schwarz, crite rion10.33771Log likelihood-5371.052Hannan-Cluinn criter.10.

13、S193SF-stati stic9.E0951JDurbin-Watson stat1.998692Pro tv(F-5tati stie0.000030VariableCoefficientStd. Errort-StatisticProb.SZA-1)-0.0057820.003-555-1.6265100.1042DSZAt-10.1056710.0315663M75710.0008C5HL7253935.339861.5297110.1264R-squared0.013063Mean dependentvar-3.114484Adjusted R-squared0.011079SLD

14、 dependentvar2091403S.E. of regression207.9785Akaike infa criterion13.51575Sum squared re-sid43038795Schwarz criterion13.53050Log likelihood-674135&Hannan-Quinn criter.13.52135F-stati sticBL5B4K3SDurbin-Watson stat-1.986906Pro tv(F-5tati stic)0.001W100200300400500600700 SOO 9001000LOGSZA LOGSHAAugme

15、nted Di ckey-Fu 11 er test stati sti c-0594408Ci.8692Test critical values:1?4i level-3.4366765% level-2.S6422210% level-2.568250MacKinnon (1996 one-si de dp-values.Augmented D i ckey-Fu 11 e r Tet E q u ati o n Dependentvariable: D(LDGSHA) Method: Least Squares Date: 05/16/18 Time: 11:28 Sample (adj

16、usted): 2 1000Included observations: 999 after adjustmentsVariableCoefficientStd. Error t-StatisticProb.LOGSHA-1)-0.0016030.002697-0.5944080.5524C0.0124-730.0216760.5756660.5650R-sq uared0.000354Mean dependentvar-0.000403Adjusted R-squared-0.000643SLD dependentvar0.015548S E. of regression0.0155&4Ak

17、a ike info criterion-5.487058Sum squared resid0.241187Schwarz criterion-5.477235Lag likelihood2742.785Hannan-Ouinn criter.-5.483324F-statistic0353321Durbin-Watson stat1.851141ProbfF-statistic)0.55274Null Hypothesis: LQGSZA has a unit rootExogenous: ConstantLag Length: 0 (Automatic - based on SIC, ma

18、xlag =21)t-StatisticProb?Augmented Dickey-Fuller test statistic-1.0943130.71 琳Test critical values:IK level-3.4366765% level-2.S6422210% level-2.56325-0MacKinnon (1995) one-sidled p-values.Augmented Dickey-Fuller Teat Equation ependentVariable: D(LOGSZA Method: Least Squares ate: 05/16/18 Time: 1113

19、2 Sample (adjusted): 2 1000Included observations: 999 after adjustmentsVariableCoefficient&td. Error1-StatistieProb.LOGSZA-1)-0.00J&950.00284-1.09481 Jd.2739C0.0329280.0304031.003054Ci.2790R-squared0.001201Mean dependlent var-0.000352Adjusted R-squared0.000199S.D. dependle nt var0.017858S.E. of regr

20、e-ssionC-.017356Akaike info criterion-5.210967Sum squared resid0517076Schwarz criterion&20T144Log likelihood2604.S75Hannan-Quinn criter.-5.207233F-statistic1.198616Durbin-Wats&n stat1.853047Prob(F-statistie)0.273863Dependent Variable: LOGSHAMethod: Least Squaresate: 05/16/1B Time: 1135Sample: 1 1000

21、Included observations: 1OOOVariableCoefficientStd. Error t-statisticProb.C-1.59374-30.061025-26.116270.0000LOG泌1.0400840.006591157.79830.0000R-s：quared0.961465Mean dependlentvar5.0J4243Adjusted R-squared0.961426S.D. de pendent var0.132B19S. E. of regression0.035906Akaike infa criterion-3.813B29Sum s

22、quared resid1.286660Schwarz criterion-3.804013Log livelihood1908.914Hannan-Quinn criter.-3.810098F-stati-stic24900.+6Durbin-Watson stat0.045051Prob(F-statistic)0.000000Null Hypothesis: RESID01 has a unit rootExogenous: ConstantLag Length: 0 (Automatic - based on SIC, maxlag =21)t-StatisticProb/Augme

23、nted Dickey-Fuller test statistic-3.3236480.0141Test critical values:1?41 level-3.4366765% level-2.86422210% level-2.56S25-0MacKinnon (1996) one-sidled p-valuesAugmented Dickey-FullerTetEquation Dependent Variable: D(RESIDai;Method: Least SquaresDate: 05/16/18 Time: 11:33Sample (adjusted): 21000Incl

24、uded observations: 999 after adjusimentsVariableCoefficientStd. Errort-StatistieProb.RESID01(-1)-0.022228o.aosBS?-3.323648Ci.0009C-3.64E-050.000240-0.15179S0.8794R-squared0.010958Mean dependle nt war-3.71 E-05Adjusted Fi-squared0.009966S.D. dependentvar0.007621S.E. ofregression0.007&83Akaike info cr

25、iterion-6.923821Sum squared resid0.05729Schwarz criterion-6.91399SLog likelihoodJ46 0.449Hannan-CiLinn criter.-6.9200S7F-siati stic11.04663Durbin-Watson stat-1.943587Pro b(F-sta-ti stie0.000921殘差resid 01檢驗(yàn)結(jié)果Null Hypothesis: RESID02 has a unit rootExogenous: ConstantLag Length: 0 (Automatic - based o

26、n SIC, maxlag =21;t-StatisticProb *Augmented Dickey-Fuller test statistic-13236430.0141Test critical values:I1% level-3.4366765% level-2S6422210% level-2.568250*MacKinnon (1996) one-sided p-valuesAugmented Dickey-Fuller Teat EquationependentVariable: D(RESIDQ2)Method; Least Squaresate: 05/16/18 Time

27、: 11:42Sample (adjusted: 21000Included observation.s: 999 after adjustmenteVariableCoefficientStd. Errort-StatisticProb.RESID 02(-1；-0.0222260.00&37-3.3236480.0009C-3.64E-050.000240-0.1517960.B794R-squared0 010958Mean dependent var-3-.71 E-05Adjusted R.-sqwared0.009966S.D. dependlentvar0.007621S.E. of regre-ssion0.007383Akai屈 info criterion-6.923S21Sum squared resid0.057329Schwarz criterion-6.913998Log likelihood3460 44-9Hannan-Quinn triter.-6.920