数据结构：

Y      X1 X2 X3 X4 0.86 0.82 1224.9 9800.3 0.01 0.54 0.81 1285.1 10979 0.03 0.13 0.8 1224.9 14584 0.03 0.16 0.8 1344 16266 0.03 0.3 0.79 1262.1 17606 0.05 0.91 0.77 1300.5 20260 0.08 0.44 0.75 1381.1 23629 0.07 0.48 0.73 1466.9 26417 0.05 0.61 0.68 1512.9 31211 0.05 0.6 0.66 1770.2 37363 0.07

 

Adf test of Y

Step 1

ADF Test Statistic

-1.24970839478

    1%   Critical Value*

-2.90752835038

 

 

    5%   Critical Value

-1.9835221635

 

 

    10% Critical Value

-1.63571110037

*MacKinnon critical values for rejection of hypothesis of a unit root.

 

 

 

 

 

 

 

 

 

 

Augmented Dickey-Fuller Test Equation

Dependent Variable: D(Y)

Method: Least Squares

Date: 10/09/08   Time: 15:27

Sample(adjusted): 2 10

Included observations: 9 after adjusting endpoints

Variable

Coefficient

Std. Error

t-Statistic

Prob. 

Y(-1)

-0.229958032928

0.184009352813

-1.24970839478

0.246726940496

R-squared

0.156314066162

    Mean dependent var

-0.0288888888889

Adjusted R-squared

0.156314066162

    S.D. dependent var

0.334493813263

S.E. of regression

0.307240521638

    Akaike info criterion

0.582067492906

Sum squared resid

0.75517390509

    Schwarz criterion

0.603981334832

Log likelihood

-1.61930371808

    Durbin-Watson stat

1.95813491942

Step 2

ADF Test Statistic

-3.11840843356

    1%   Critical Value*

-2.96767495573

 

 

    5%   Critical Value

-1.9890499413

 

 

    10% Critical Value

-1.63822498918

*MacKinnon critical values for rejection of hypothesis of a unit root.

 

 

 

 

 

 

 

 

 

 

Augmented Dickey-Fuller Test Equation

Dependent Variable: D(Y,2)

Method: Least Squares

Date: 10/09/08   Time: 15:30

Sample(adjusted): 3 10

Included observations: 8 after adjusting endpoints

Variable

Coefficient

Std. Error

t-Statistic

Prob. 

D(Y(-1))

-1.10315789474

0.353756705782

-3.11840843356

0.0168812689653

R-squared

0.578772835346

    Mean dependent var

0.03875

Adjusted R-squared

0.578772835346

    S.D. dependent var

0.517809603729

S.E. of regression

0.336068870493

    Akaike info criterion

0.773467337149

Sum squared resid

0.790596

    Schwarz criterion

0.783397529859

Log likelihood

-2.09386934859

    Durbin-Watson stat

2.15240153153

Y 是一阶单整；

 

Adf test of X1

ADF Test Statistic

-3.56753212396

    1%   Critical Value*

-2.90752835038

 

 

    5%   Critical Value

-1.9835221635

 

 

    10% Critical Value

-1.63571110037

*MacKinnon critical values for rejection of hypothesis of a unit root.

 

 

 

 

 

 

 

 

 

 

Augmented Dickey-Fuller Test Equation

Dependent Variable: D(X1)

Method: Least Squares

Date: 10/09/08   Time: 15:32

Sample(adjusted): 2 10

Included observations: 9 after adjusting endpoints

Variable

Coefficient

Std. Error

t-Statistic

Prob. 

X1(-1)

-0.0224026154961

0.00627958339761

-3.56753212396

0.00731993746544

R-squared

-0.0917286528975

    Mean dependent var

-0.0177777777778

Adjusted R-squared

-0.0917286528975

    S.D. dependent var

0.0139443337756

S.E. of regression

0.0145698514542

    Akaike info criterion

-5.51528545532

Sum squared resid

0.00169824457117

    Schwarz criterion

-5.49337161339

Log likelihood

25.8187845489

    Durbin-Watson stat

1.21400817987

X1 没有单位根

 

Adf test of X2

ADF Test Statistic

2.88906002271

    1%   Critical Value*

-4.64050620794

 

 

    5%   Critical Value

-3.33497487009

 

 

    10% Critical Value

-2.81685004383

*MacKinnon critical values for rejection of hypothesis of a unit root.

 

 

 

 

 

 

 

 

 

 

Augmented Dickey-Fuller Test Equation

Dependent Variable: D(X2)

Method: Least Squares

Date: 10/09/08   Time: 15:36

Sample(adjusted): 3 10

Included observations: 8 after adjusting endpoints

Variable

Coefficient

Std. Error

t-Statistic

Prob. 

X2(-1)

0.976807507209

0.338105646656

2.88906002271

0.0342243059951

D(X2(-1))

-1.24180336229

0.480653515137

-2.58357282987

0.0492185263564

C

-1210.60044258

446.432624705

-2.71172037074

0.0421894835766

R-squared

0.657254246897

    Mean dependent var

60.6375

Adjusted R-squared

0.520155945656

    S.D. dependent var

106.068077027

S.E. of regression

73.4741810848

    Akaike info criterion

11.7117415707

Sum squared resid

26992.2764304

    Schwarz criterion

11.7415321488

Log likelihood

-43.8469662826

    F-statistic

4.79403640269

Durbin-Watson stat

2.6241221641

    Prob(F-statistic)

0.0687749376894

X2 在假设存在常数项的情况下检验，在95%的概率下通过：没有单位根。但在没有常数项的情况下检验在95%概率下不通过，在90%的概率下通过没有单位根。

 

Adf test of X3

ADF Test Statistic

2.60687487097

    1%   Critical Value*

-2.96767495573

 

 

    5%   Critical Value

-1.9890499413

 

 

    10% Critical Value

-1.63822498918

*MacKinnon critical values for rejection of hypothesis of a unit root.

 

 

 

 

 

 

 

 

 

 

Augmented Dickey-Fuller Test Equation

Dependent Variable: D(X3)

Method: Least Squares

Date: 10/09/08   Time: 15:39

Sample(adjusted): 3 10

Included observations: 8 after adjusting endpoints

Variable

Coefficient

Std. Error

t-Statistic

Prob. 

X3(-1)

0.184309286735

0.0707012403191

2.60687487097

0.0402889270165

D(X3(-1))

-0.14502614751

0.510141739643

-0.284285986109

0.785747463303

R-squared

0.549403573406

    Mean dependent var

3298

Adjusted R-squared

0.474304168974

    S.D. dependent var

1585.77056528

S.E. of regression

1149.7611205

    Akaike info criterion

17.1448139509

Sum squared resid

7931703.80529

    Schwarz criterion

17.1646743363

Log likelihood

-66.5792558036

    Durbin-Watson stat

1.36753313325

X3在假设没有常数项的前提下没有单位根（95%）

 

Adf test of X4

ADF Test Statistic

-2.71416039811

    1%   Critical Value*

-3.05069791541

 

 

    5%   Critical Value

-1.99615708419

 

 

    10% Critical Value

-1.64145713193

*MacKinnon critical values for rejection of hypothesis of a unit root.

 

 

 

 

 

 

 

 

 

 

Augmented Dickey-Fuller Test Equation

Dependent Variable: D(X4,2)

Method: Least Squares

Date: 10/09/08   Time: 15:41

Sample(adjusted): 4 10

Included observations: 7 after adjusting endpoints

Variable

Coefficient

Std. Error

t-Statistic

Prob. 

D(X4(-1))

-1.19137466307

0.438947773279

-2.71416039811

0.0420668502387

D(X4(-1),2)

0.649595687332

0.340007483153

1.91053350152

0.114308014409

R-squared

0.595163949441

    Mean dependent var

0.00285714285714

Adjusted R-squared

0.51419673933

    S.D. dependent var

0.0221466970557

S.E. of regression

0.0154361566659

    Akaike info criterion

-5.26925197073

Sum squared resid

0.00119137466307

    Schwarz criterion

-5.28470621386

Log likelihood

20.4423818976

    Durbin-Watson stat

1.08138088327

X4存在单位根，一阶单整。

结论：Y和X4 是一阶协整，X1、X2、X3不存在单位根。

 

滞后一阶的Granger Causality

Pairwise Granger Causality Tests

Date: 10/09/08   Time: 15:47

Sample: 1 10

Lags: 1

  Null Hypothesis:

Obs

F-Statistic

Probability

  X1 does not Granger Cause Y

9

0.892535272818

0.381263630894

  Y does not Granger Cause X1

0.131547115503

0.729267123282

  X2 does not Granger Cause Y

9

0.432613131431

0.535113716964

  Y does not Granger Cause X2

0.415712630321

0.542934145248

  X3 does not Granger Cause Y

9

1.33973024694

0.291073178046

  Y does not Granger Cause X3

1.04591385816

0.345902054529

  X4 does not Granger Cause Y

9

0.467395725164

0.519702590718

  Y does not Granger Cause X4

0.0227796409288

0.884977974178

  X2 does not Granger Cause X1

9

1.15035840082

0.324706204896

  X1 does not Granger Cause X2

34.6441983879

0.00106648026535

  X3 does not Granger Cause X1

9

1.12236905291

0.330182772381

  X1 does not Granger Cause X3

6.07625792641

0.0487869671525

  X4 does not Granger Cause X1

9

0.222451395114

0.653840846121

  X1 does not Granger Cause X4

0.42553581166

0.538360947319

  X3 does not Granger Cause X2

9

4.95581960724

0.0676215894838

  X2 does not Granger Cause X3

1.01466184177

0.352669808582

  X4 does not Granger Cause X2

9

0.161436072031

0.701758373975

  X2 does not Granger Cause X4

0.186727991496

0.680751760998

  X4 does not Granger Cause X3

9

0.0868040049626

0.77820814714

  X3 does not Granger Cause X4

0.636019038333

0.455549633303

 

滞后2阶的GrangerCausality

Pairwise Granger Causality Tests

Date: 10/09/08   Time: 15:46

Sample: 1 10

Lags: 2

  Null Hypothesis:

Obs

F-Statistic

Probability

  X1 does not Granger Cause Y

8

0.584878210387

0.610261332436

  Y does not Granger Cause X1

1.14818632405

0.426298771351

  X2 does not Granger Cause Y

8

1.36107300581

0.379615099809

  Y does not Granger Cause X2

0.441952151239

0.678858251548

  X3 does not Granger Cause Y

8

1.91892672661

0.290604408789

  Y does not Granger Cause X3

0.843719143888

0.512010111097

  X4 does not Granger Cause Y

8

0.666077930153

0.576269683126

  Y does not Granger Cause X4

1.7527671387

0.313153613806

  X2 does not Granger Cause X1

8

0.0367374212119

0.964356002817

  X1 does not Granger Cause X2

7.61611554935

0.0667455254798

  X3 does not Granger Cause X1

8

1.04865847326

0.45151213222

  X1 does not Granger Cause X3

10.7641725128

0.0427739652534

  X4 does not Granger Cause X1

8

0.334397165872

0.739429601203

  X1 does not Granger Cause X4

3.03322210305

0.190338390297

  X3 does not Granger Cause X2

8

11.3572530864

0.0398487405196

  X2 does not Granger Cause X3

0.921972690861

0.487397195278

  X4 does not Granger Cause X2

8

0.284097508228

0.770919460124

  X2 does not Granger Cause X4

1.29547903996

0.393054278525

  X4 does not Granger Cause X3

8

0.707109053423

0.560274943226

  X3 does not Granger Cause X4

2.67795356189

0.215125293511

GrangerCausality 对阶数比较敏感，因而需要更多的数据，考察在多滞后几阶的情况下结论的变化情况。本例每组只有10个数据，最多滞后2阶能得到因果检验的结果，3阶及以上是不能做的。

因果关系的结论是：X1对X2、X3有Granger因果关系（1阶和2阶，90%），X3对X2有因果关系（2阶，95%），重要的结论处我已经用颜色标记出来了，请查阅。欢迎交流～

这是Word版本的解题过程，供参考～～

请将回复设置成出售帖，这样我就可以付钱了，非常感谢您的回复,对了，我怎么没看到协整啊

[此贴子已经被作者于2008-10-9 21:36:27编辑过]

不好意思，忘了。。。补发一下协整的检验

已经补发上了，欢迎随时跟我交流～

能不能问一下，这是什么研究项目的呀？