计量经济学-时间序列

（二）图形分析

通过对样本数据做散点图（图1、图2）发现，匕与&、后呈近似直线关系，根据图3

的趋势图，三者同趋势变化，考虑时间序列模型，初步判断其不平稳，存在二阶可能性。于

是得到该模型的理论方程为：

YFBB2X21+u$（1）

式中，〃，为随机误差项，描述变量外的因素对模型的干扰；历为样本回归函数的截距

系数；氏、氏为样本回归函数的斜率系数；下标t为年份，t二1990,1991,…，2010o

图1丫与X1散点图图2丫与X2散点图

图3趋势图

（三）单位根检验

表2单位根检验表

变量检验方程ADF值P平稳性阶数

匕(c,t,2)3.3191.0000不平稳

(c,0,4)2.7330.9999不平稳

(0,0.4)2.8550.9973不平稳

△匕(c,t,3)-1.6680.7178不平稳

(c,0.2)2.1570.9997不平稳

(0,0,2)3.6670.9996不平稳

△2K(c,t,1)-5.9240.0010平稳〜I⑵

x,t(c,t,4)0.9440.9995不平稳

(c,0,4)3.4051.0000不平稳

(0.0.4)3.4480.9992不平稳

△乂(c,t,3)-2.0790.5178不平稳

(c.0.4)0.7570.9891不平稳

(0,0,4)1.2740.9404不平稳

△2Zt(c,t,4)-3.9630.0381平稳〜I⑶

(c,t,4)不平稳

x2t4.9971.0000

(c,0,0)8.6581.0000不平稳

(0.0.0)14.1741.0000不平稳

△公(c,t,0)-2.4860.3303不平稳

(c,0.4)2.9261.0000不平稳

(0,0,4)2.8920.9974不平稳

(c,t,1)-4.8750.0063平稳〜I⑶

经过差分后,匕与％r、公均平稳,但是匕为二阶单整,九、照三阶单整，可能存在线性后

降阶，因此可以尝试建立回归模型。

(四)建立回归模型

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

图4第一次模型

2.自相关性检验

(1)残差图分析：

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

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

图5残差图

(2)DW检验：

a=0.05,k=2,查表得到出=1.125,因为DW=0.678小于小，因此存在一阶自相关性,

(=]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

图6DW检验

(3)偏相关系数检验:

[=]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

图7偏相关洗漱检验

由图可见，当绝对值PAC大于0.5时，即超出PC图中虚线部分时，存在一阶自相关性。

(4)BG检验:

[=]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

▼

图8BG检验

nRJ8.3277,临界概率0.0155小于0.05,因此拒绝假设H。,存在自相关性。又因为ei

回归系数显著不为0,因此模型存在一阶自相关性。

3.自相关性处理

得到调整后的方程：

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

简化后：

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

图9调整后方程

4.调整后自相关性检验

（1）调整后偏相关系数检验:

[=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

图10调整后偏相关系数检验

经调整，PC图中不存在超出虚线部分，说明自相关性已消除。

(2)调整后BG检验：

[=]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

图11调整后BG检验

因为*2的临界概率0.9928已经非常大，大于0.05,因此接受假设H。，不存在自相关性。

5.异方差检验:

[=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

图12WHITE检验

因为显著性水平a=0.05,nR?的概率0.0813大于0.05,落入接受域，原假设成立