計(jì)量經(jīng)濟(jì)學(xué)-時(shí)間序列

（二）圖形分析

通過(guò)對(duì)樣本數(shù)據(jù)做散點(diǎn)圖（圖1、圖2）發(fā)現(xiàn)，匕與&、后呈近似直線關(guān)系，根據(jù)圖3

的趨勢(shì)圖，三者同趨勢(shì)變化，考慮時(shí)間序列模型，初步判斷其不平穩(wěn)，存在二階可能性。于

是得到該模型的理論方程為：

YFBB2X21+u$（1）

式中，〃，為隨機(jī)誤差項(xiàng)，描述變量外的因素對(duì)模型的干擾；歷為樣本回歸函數(shù)的截距

系數(shù)；氏、氏為樣本回歸函數(shù)的斜率系數(shù)；下標(biāo)t為年份，t二1990,1991,…，2010o

圖1丫與X1散點(diǎn)圖圖2丫與X2散點(diǎn)圖

圖3趨勢(shì)圖

（三）單位根檢驗(yàn)

表2單位根檢驗(yàn)表

變量檢驗(yàn)方程ADF值P平穩(wěn)性階數(shù)

匕(c,t,2)3.3191.0000不平穩(wěn)

(c,0,4)2.7330.9999不平穩(wěn)

(0,0.4)2.8550.9973不平穩(wěn)

△匕(c,t,3)-1.6680.7178不平穩(wěn)

(c,0.2)2.1570.9997不平穩(wěn)

(0,0,2)3.6670.9996不平穩(wěn)

△2K(c,t,1)-5.9240.0010平穩(wěn)?I⑵

x,t(c,t,4)0.9440.9995不平穩(wěn)

(c,0,4)3.4051.0000不平穩(wěn)

(0.0.4)3.4480.9992不平穩(wěn)

△乂(c,t,3)-2.0790.5178不平穩(wěn)

(c.0.4)0.7570.9891不平穩(wěn)

(0,0,4)1.2740.9404不平穩(wěn)

△2Zt(c,t,4)-3.9630.0381平穩(wěn)?I⑶

(c,t,4)不平穩(wěn)

x2t4.9971.0000

(c,0,0)8.6581.0000不平穩(wěn)

(0.0.0)14.1741.0000不平穩(wěn)

△公(c,t,0)-2.4860.3303不平穩(wěn)

(c,0.4)2.9261.0000不平穩(wěn)

(0,0,4)2.8920.9974不平穩(wěn)

(c,t,1)-4.8750.0063平穩(wěn)?I⑶

經(jīng)過(guò)差分后,匕與％r、公均平穩(wěn),但是匕為二階單整,九、照三階單整，可能存在線性后

降階，因此可以嘗試建立回歸模型。

(四)建立回歸模型

1.LSYCX1X2

得到方程：Y=-3725.7829016+0.350915608536*X1+0.116993116659*X2

t：(-4.260)(8.438)(2.180)

〃二0.998,DW=0.678,F=6857.838

[=]Equation:UNBTLEDWorkfileUNHTLED::Untitled\_BX

[view|PfocjObject|Print[Name[Freeze]〔Estimate〔Forecast卜atts〔Resid；

DependentVariable:Y

Method:LeastSquares

Date:12/16/15Time:20:36

Sample:19902010

Includedobservations:21

VariableCoefficientStd.Errort-StatlstlcProb.

c-3725783874.6747-4.2596210.0005

X10.3509160.0415858/384400.0000

X20.1169930.0536572.1803920.0427

R-squared0998689Meandependentvar5553603

AdjustedR-squared0.998544S.D.dependentvar48890.05

S.E.ofregression1865.701Akaikeinfocriterion18.03222

3umsquaredresid6265512GSchwarzcriterion18.18144

Loglikelihood-186.3384Hannan-Quinncriter.1806461

F-statistic6857.838Durbin-Watsonstat0.678223

ProD(F-statistic)0.000000

圖4第一次模型

2.自相關(guān)性檢驗(yàn)

(1)殘差圖分析：

[=1Equation:UNTITLEDWorkfile:UNTITLED::Untitled\-OX

|viewkroc[objed]〔Print[Name〔Freeze]〔Estimate[Forecast]StatsResids

圖5殘差圖

(2)DW檢驗(yàn)：

a=0.05,k=2,查表得到出=1.125,因?yàn)镈W=0.678小于小，因此存在一階自相關(guān)性,

(=]Equation:UNBTLEDWorkfileUNTTTLED::Untitled\_BX

[view]pfoc[objed|PrintjName|FreezejEstimate|ForecastJstatS^Resid￡

DependentVarable:Y

Method:LeastSquares

Date:12/16/15Time:20:36

Sample:19902010

Includedobservations:21

VariableCoeffiaentStd.Errort-SlatistlcProb.

C-3725783874.6747-4.2596210.0005

X10.3509160.0415858.4384400.0000

X20.1169930.0536572.1803920.0427

R-squared0998689Meandependentvar5553603

AdjustedR-sqiared0.998544S.D.dependentvar48890.05

S.E.ofregression1865.701Akaikeinfocriterion18.03222

Sumsquaredresid62655126Schwarzcriterion18.18144

Loglikelihood-186.3384Hannan-Quinncriter.1806461

F-statistic6857.838Durbin-Watsonstat0.678223

Prob(F-statistic)0.000000

圖6DW檢驗(yàn)

(3)偏相關(guān)系數(shù)檢驗(yàn):

[=]Equation:UNITTLEDWorkfile:UNKTLED::Untitled\-BX

|View|ProcObject(PrintNameFreeze?EstimateForecastStatsResids

CorrelooramofResiduals

Date:12/16/15Time:21:50

Sample:19902010

Includedobservations:21

AutocorrelationPartialCorrelationACPACQ-StatProb

i____IiI____110.5990.5998.66310.003

?Zl??□?20.252-0.16610.2780.006

?匚?U?3-0.157-0.37410.9370.012

[=?i匚i4-0.460-0.30016.9610.002

[1?115-0.4570.06023.2640.000

1匚1?]?6-0.2730.11125.6690.000

11?]'70.0140.08225.6750.001

1Zl1?1180.226-0.04227.5780.001

1=]1?L?90.270-0.10030.5180.000

1ZJ??□1100.148-0.10631.4830.000

111??11-0.045-0.03531,5800.001

?d1?l|112-0.220-0.03534.1860.001

圖7偏相關(guān)洗漱檢驗(yàn)

由圖可見(jiàn)，當(dāng)絕對(duì)值PAC大于0.5時(shí)，即超出PC圖中虛線部分時(shí)，存在一階自相關(guān)性。

(4)BG檢驗(yàn):

[=]Equation:UNITTLEDWorkfile:UNTITLED::Untitled\_BX

View[ProcObject|PrintName[Freeze|EstimateIForecast?StatsResids

Breusch-GcdfreySerialCorrelationLMTest:*

F-statistic5.257218Prob.F(2,16)0.0176

Obs,R-squared8.327658Prob.Chi-Square(2)0.0155

TestEquation:

Dependentvariable:RESID

Method:LeastSquares

Date:12/16/15Time:21:58

Sample:19902010

Includedobsen/ations:21

Presamplemissingvaluelaggedresidualssettozero.

VariableCoefficientStd.Errort-StatisticF—

C-250.0119794.3014-0.3147570.7570

X10.0125940.0379270.3320610.7442

X2-0.0151200.048329-0.3128610.7584

RESID(-1)0.7059900.2490152.8351290.0119

RESID(-2)-0.1043010.289007-0.3608950.7229

R-squared0396555Meandependentvar143E-12

AdjustedR-squared0.245694S.D.dependentvar1769.959

S.E.ofregression1537.224Akaikeinfocriterion17.71760

Sumsquaredresid37808914Sctiwarzcrilerion17.96630

Loglikelihood-181.0348Hannan-Quinncriter.17.77157

F-statistic2.628609Durbin-Watsonstat1.928180

Prob(F-statistic)0.073365

▼

圖8BG檢驗(yàn)

nRJ8.3277,臨界概率0.0155小于0.05,因此拒絕假設(shè)H。,存在自相關(guān)性。又因?yàn)閑i

回歸系數(shù)顯著不為0,因此模型存在一階自相關(guān)性。

3.自相關(guān)性處理

得到調(diào)整后的方程：

Y=-5417.76973503+0.390265879342*X1+0.0736268142467*X2+[AR(1)=0.668162678879]

簡(jiǎn)化后：

Y=-5417.77+0.39*Xi+0.07*X2+[AR(1)=0.67]

t=(11.594)(1.755)(3.759)

口;0.999,DW-1.953,F-7829.251

(=)Equation:UNTITLEDWorkfile:UNTnLED::Untitled\_nX

(ViewProcObject|PrintNameFreezeEstimateForecastStatsResids

DependentVariable:Y

Method:LeastSquares

Date:12/16/15Time:22:10

Sample(adjusted):19912010

Includedobservations:20afteradjustments

Convergenceachievedafter7iterations

VariableCoefficientStd.Errort-StatisticProb.

C-5417.7701808.200-2.9962230.0085

X10.3902660.03366211.593680.0000

X20.0736270.0419591.7547510.0984

AR(1)0.6681630.1777433.7591550.0017

R-squared0.999319Meandependentvar58018.42

AdjustedR-squared0.999192S.D.dependentvar48783.41

S.E.ofregression1387.012Akaikeinfocriterion17.48455

Sumsquaredresid30780858Sciiwarzcriterion17.68369

Loglikelihood-170.8455Hannan-Quinncriter.17.52342

F-statistic7829.251Durbin-Watsonstat1.952757

Prob(F-statistic)0.000000

InvertedARRoots.67

圖9調(diào)整后方程

4.調(diào)整后自相關(guān)性檢驗(yàn)

（1）調(diào)整后偏相關(guān)系數(shù)檢驗(yàn):

[=1Equation:UNTITLEDWorkfile:UNHTLED::Untitled\_□X

[viewProc|Object]Print

NameFreeze|EstimateForecastStatsResids

CorrelogramofResiduals

Date:12/17/15Time:15:10

Sample:19912010

Includedobservations:20

Q-statisticprobabilitiesadjustedfor1ARMAterm(s)

AutocorrelationPartialCorrelationACPACQ-StatProb

'I'1111-0.001-0.0014.E-05

?□?I3120.1900.1900.87960.348

'匚??匚13-0.277-0.2872.87040.238

'[=?1二14-0.337-0.4055.99630.112

'匚?1匚15-0.340-0.3219.38300.052

?匚??匚16-0.199-0.26210.6280.059

III?E?70.058-0.13710.7430.097

IZ]I11180.234-0.03412.7530.078

I=]I11190.287-0.03516.0480.042

I□I?C1100.180-0.11017.4710.042

IIIIC1110.040-0.11217.5480.063

II1112-0.101-0.05218.1130.079

圖10調(diào)整后偏相關(guān)系數(shù)檢驗(yàn)

經(jīng)調(diào)整，PC圖中不存在超出虛線部分，說(shuō)明自相關(guān)性已消除。

(2)調(diào)整后BG檢驗(yàn)：

[=]Equation:UNTITLEDWorkfile:UNTITLED::Untitled\-0X

ViewProcObjectPrintNameFreeze||EstimateForecastStatsResids

Breusch-GodfreySerialCorrelationLMTest

F-statistic6.14E-05Prob.F(1,15)0.9939

Obs*R-squared8.19E-05Prob.Chi-Square(l)0.9928

TestEquation:

DependentVariable:RESID

Method:LeastSquares

Date:12/17/15Time:15:16

Sample:19912010

Includedobservations:20

Presamplemissingvaluelaggedresidualssettozero.

VariableCoefficientStd.Errort-StatisticProb.

C-9.2827302211.779-0.0041970.9967

X18.27E-050.0363340.0022770.9982

X2-5.96E-050.043997-0.0013550.9989

AR⑴0.0016860.2828990.0059600.9953

RESID(-1)-0.0031350.400070-0.0078350.9939

R-squared0.000004Meandependentvar-1.33E-07

AdjustedR-squared-0.266661S.D.dependentvar1272.810

S.E.ofregression1432.497Akaikeinfocriterion17.58454

Sumsquaredresid30780732Schwarzcriterion17.83348

▼

IAHlilrQlihnn/i-170JMA/IU-lonnonlinnrritor17AQQ44

圖11調(diào)整后BG檢驗(yàn)

因?yàn)?2的臨界概率0.9928已經(jīng)非常大，大于0.05,因此接受假設(shè)H。，不存在自相關(guān)性。

5.異方差檢驗(yàn):

[=JEquation:UNTITLEDWorkfile:UNTITLED::Untitled\_n1

View|ProcObject|PrintNameFreezeEstimateForecastStatsResids

HeteroskedastidtyTest:White

F-statistic3.685659Prob.F(9.10)0.0271

Obs'R-squared15.36725Prob.Chi-Square(9)0.0813

ScaledexplainedSS6.010028Prob.Chi-Square(9)0.7389

TestEquation:

DependentVariable:RESIDE

Method:LeastSquares

Date:12/17/15Time:14:50

Sample:19912010

Includedobservations:20

Collineartestregressorsdroppedfromspecification

圖12WHITE檢驗(yàn)

因?yàn)轱@著性水平a=0.05,nR?的概率0.0813大于0.05,落入接受域，原假設(shè)成立