6.3——1.分析比較股票市場繁榮程度與宏觀經(jīng)濟(jì)運(yùn)行情況之間的關(guān)

系，建立估計回歸模型：

Yt邛i+BzXt+W

式中，九表示股票價格指數(shù);凡表示國內(nèi)生產(chǎn)總值(10億美元)。

(1)利用Eviews做回歸分析:

ViewProcObjectPrintNameFreezeEstimateForecastStatsResids

DependentVariable:Y

Method:LeastSquares

Date:12/02/17Time:11:43

Sample:19812006

Includedobservations:26

VariableCoefficientStd.Errort-StatisticProb.

C-2123.864324.8012-6.5389660.0000

X0.7841060.04127618.996800.0000

R-squared0.937643Meandependentvar3604.775

AdjustedR-squared0.935044S.D.dependentvar2414.000

S.E.ofregression615.2413Akaikeinfocriterion15.75571

Sumsquaredresid9084525.Schwarzcriterion15.85249

Loglikelihood-202.8242Hannan-Quinncriter.15.78358

F-statistic360.8784Durbin-Watsonstat0.440822

Prob(F-statistic)0.000000

模型估計結(jié)果：rt=-2123.864+0.784106Xt

(324.8012)(0.041276)

t二(-6.538966)(18.99680)

R2=0.937643F=360.8784DW=

0.440822

(2)自相關(guān)的檢驗(yàn)

①圖示檢驗(yàn)法

1.500

1.000

500

IU0

-500

?1.000

-1.500

-1,500-1.000-500)5001,0001,500

從上圖可以看出，大部分點(diǎn)都落在1,3象限，表明隨機(jī)誤差項(xiàng)上

存在正自相關(guān)。

②BG檢驗(yàn)

ViewjProc|Object||PrintName|Freezej|Estimate〔Forecast〔Stats]ResidsJ

Breusch-GodfreySerialCorrelationLMTest:

F-statistic37.41424Prob.F(2,22)0.0000

Obs,R-squared20.09265Prob.Chi-Square(2)0.0000

TestEquation:

DependentVariable:RESID

Method:LeastSquares

Date:12/02/17Time:11:52

Sample:19812006

Includedobservations:26

Presamplemissingvaluelaggedresidualssettozero.

VariableCoefficientStd.Errort-Statis1icProb.

C-38.62611161.7673-0.2387760.8135

X0.0067190.0205650.3267280.7470

RESID(-1)1.2967020.1615398.0271920.0000

RESID(-2)-0.6815590.162165-4.2028630.0004

R-squared0.772794Meandependentvar-1.89E-13

AdjustedR-squared0.741812SDdependentvar602.8109

S.E.ofregression306.3018Akaikeinfocriterion14.42766

Sumsquaredresid2064057.Schwarzcriterion14.62121

Loglikelihood-183.5595Hannan-Quinncriter14.48339

F-statistic24.94283Durbin-Watsonstat2.224598

Prob(F-statistic)0.000000

由上圖可知LM=77?2=26*0.772794二20.09265＞入常,=5.9915

V/?VZKJ

且PR.OOOOVa=0.05,表明存在自相關(guān)。通過LM檢驗(yàn)的結(jié)果可知

與e.2的t檢驗(yàn)均顯著，所以判斷為二階自相關(guān)。

(3)修正自相關(guān)

①廣義差分法

在EViews命令欄中輸入“Isee(7)”得到估計方程

^f—0.768816e《_]

對原模型進(jìn)行廣義差分回歸：

Yt-Q.768816y(1-0.768816)+/?2(XrO.768816X1)

十%

在Eviews中得到廣義差分回歸的輸出結(jié)果:

ViewProcObjectPrintNameFreezeEstimateForecastStatsResids

DependentVariable:Y-0.779589*Y(-1)

Method:LeastSquares

Date:12/02/17Time:12:13

Sample(adjusted):19822006

Includedobservations:25afteradjustments

VariableCoefficientStd.Errort-StatisticProb.

C-634.1843220.3997-2.8774290.0085

X-0.779589*X(-1)0.8616960.1052518.1870540.0000

R-squared0.744524Meandependentvar1055.640

AdjustedR-squared0.733416S.D.dependentvar748.5019

S.E.ofregression386.4649Akaikeinfocriterion14.82858

Sumsquaredresid3435168.Schwarzcriterion14,92609

Loglikelihood-183.3572Hannan-Quinncriter.14.85562

F-statistic67.02786Durbin-Watsonstat0.908327

Prob(F-statistic)0.000000

模型估計結(jié)果：埒=-634?1843+0.861696X；

€?v

(220.3997)(0.105251)

t=(-2.877429)(8.187054)

R2=0.744524,F=67.02786DW=

0.908327

式中，丫；二九一0.779589Y.i,X；=X「0.779589X.1

對廣義差分法做BG檢驗(yàn)

Q*~一———J———一-一?---———w~~----—V——-----—―■■■—---------*--

View]Proc]Object]|Print|NamejFreexe|EstimateJForecast|StatsjResids|

Breusch-GodfreySerialCorrelationLMTest:

F-statistic5.880240Prob.F(2.21>0.0094

Ot>s*R-squared8.974594產(chǎn)rodChi-Square(2)0.0113

TestEquation:

DependentVariable:RESID

Method:LeastSquares

Date:12702/17Time:12:14

Sample:19822006

Includedobservations:25

Rresamplemissingvaluelaggedresidualssettozero

VariableCoefficientStd.Errort-StatisticProb.

C-10.01218185.8390-0.0538760.9575

X-O.779589*X(-1)0.0073830.0889210.0830310.9346

RESID(-1>0.7161900.2109323.3953510.0027

RESIDC-2)-0.3068980.212092-14470020.1627

R-squared0.358984Meandependentvar3.32E-13

AdjustedR-squared0.267410SO.dependentvar3783279

S.E.ofregression323.8164Akaikeinfocriterion14.54388

Sumsquaredresid2201998.Schwarzcriterion14.73890

Loglikelihood-177.7985Hannan-Quinncriter.14.59797

F-statistic3.920160Durbin-Watsonstat2.164173

RroDCF-statistic)0.022820

由上圖可知LM=77?2=8.9746>A2=5.9915且PR.022823=

U?UD

0.05,表明存在自相關(guān)。

由于使用了廣義差分?jǐn)?shù)據(jù)，樣本容量減少了一個，為25個。查

5%顯著水平的DW統(tǒng)計表可知（二1?288,八=1.454,模型中D

W=O.902421<1.288=dL,表明該模型依然存在自相關(guān)關(guān)系，也

說明可能為高階自相關(guān)

使用科克倫-奧科特迭代法進(jìn)行廣義差分回歸:

|v'ew[PTO<[ORect][Prlr?金[Name[產(chǎn)reezeJ[Estimate[產(chǎn)orec.Resids

DependentVariable:Y

Method:LeastSquares

Date:12/02/17Time:13:25

Sample(adjusted):19832006

Includedobservations:24afteradjustments

Convergenceachievedafter4iterations

VariableCoetTicientStd.Errort-StatisticProD.

C-2354292475.5444-49507290.0001

X0.8162880.05875213.893800.0000

AR(1)1.3309900.1617888.2267380.0000

ARC2)-0.7064950.160716-4.3959250.0003

R-squared0.986286Meandependentvar3842.195

AdjustedR-squared0.984229S.D.dependentvar2359.960

S.E.ofregression296.3658Akaikeinfocriterion14.37208

Sumsquaredresid1756654.Schwarz.criterion14.56842

Loglikelihood-168.4649Hannan-Quinncriter.14.42417

F-statistic479.4716Durbin-Watsonstat2.211620

ProE>(F-statistic)0.000000

invertedARRoots.67-^.511.67-511

旌=-2354.292+0.8162884

(475.5444)(0.058753)

t=(-4.950729)(13.8938)

R2=0.986286,F=479.4716DW=2.21162

在用BG對上述方程檢驗(yàn)

Breusch-GodfreySerialCorrelationLMTest:

F-statistic0.350931Prob.F(2,18)0.7087

Obs*R-squared0.900697Prob.Chi-Square(2)0.6374

TestEquation:

DependentVariable:RESID

Method:LeastSquares

Date:12/02/17Time:13:31

Sample:19832006

Includedobservations:24

Presamplemissingvaluelaggedresidualssettozero.

VariableCoefficientStd.Errort-StatisticProb.

C8.192139501.33990.0163400.9871

X0.0007820.0631690.0123750.9903

AR(1)