金融计量学例题.doc

中国香港股市模型
一、 研究目的
研究中国香港股市变化规律，分析影响股价变动的主要因素。
二、 影响因素分析
被解释变量Y是香港恒生指数，影响因素主要从以下三个方面考虑：
（1） 股票市场自身交易情况，用成交额X1（百万美元）综合反映。
（2） 国民经济发展状况，除了反映经济发展水平的人均生产总值X2(现价美元）之外，由于不动产是香港投资上致富的主要源泉，房地产交易也是香港经济十分重要的组成部分，因此要考虑另外两个影响因素：建筑业总开支X3（百万美元）和房地产买卖金额X4（百万美元），以便分析整个国民经济以及各个重要组成部分的发展对香港股市的影响
（3） 金融环境的变化，取九九金价X5（美元/两）、港汇指数x6、优惠利率X7等因素，从贵金属、汇率、利率等方面反映金融环境对香港股价波动的影响。
恒生指数及其影响因素的统计资料

恒生指数
成交额
人均生
产总值
建筑业
总开支
房地产
买卖金额
九九金价
港汇指数
利率

y
x1
x2
x3
x4
x5
x6
x7
1991
172.9
11246
10183
4110
11242.5
681
105.9
9
1992
352.94
10335
10414
3996
12693.94
791
107.4
6.5
1993
447.67
131156
13134
4689
16681.34
607
114.4
6
1994
404.02
6127
15033
6876
22131.88
714
110.8
4.75
1995
409.51
27419
17389
8636
31353.64
911
99.4
4.75
1996
619.17
25633
21715
12339
43528.81
1231
91.1
9.5
1997
1121.17
95684
27075
16623
70752.98
2760
90.8
10
1998
1506.84
105987
31827
19937
125989.84
2651
86.3
16
1999
1105.79
46230
35393
24787
99468.48
2105
125.3
10.5
2000
933.03
37165
38832
25112
82478.3
3030
107.4
10.5
2001
1008.54
48787
46079
24414
54936.3
2810
106.6
8.5
2002
1567.56
75808
47871
22970
87135.51
2649
115.7
6
2003
1960.06
123128
54372
24403
129884.03
3031
110.1
6.5
2004
2884.88
371406
65602
30531
163044.2
3644
105.8
5
2005
2556.72
198569
74917
37861
215033.62
3690
101.6
5.25

三、 多重共线性分析
可用逐步回归法进行变量选择
Dependent Variable: Y
Method: Least Squares
Date: 12/20/09 Time: 22:07
Sample: 1974 1988
Included observations: 15
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
493.6722
158.5363
3.113937
0.0082
X1
0.007337
0.001244
5.895809
0.0001
R-squared
0.727809
Mean dependent var
1136.720
Adjusted R-squared
0.706871
S.D. dependent var
823.0463
S.E. of regression
445.6086
Akaike info criterion
15.16032
Sum squared resid
2581372.
Schwarz criterion
15.25473
Log likelihood
-111.7024
F-statistic
34.76056
Durbin-Watson stat
1.327326
Prob(F-statistic)
0.000053

Dependent Variable: Y
Method: Least Squares
Date: 12/20/09 Time: 22:09
Sample: 1974 1988
Included observations: 15
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
-147.2516
151.9300
-0.969207
0.3501
X2
0.037776
0.003865
9.773950
0.0000
R-squared
0.880218
Mean dependent var
1136.720
Adjusted R-squared
0.871004
S.D. dependent var
823.0463
S.E. of regression
295.6060
Akaike info criterion
14.33950
Sum squared resid
1135978.
Schwarz criterion
14.43390
Log likelihood
-105.5462
F-statistic
95.53011
Durbin-Watson stat
1.389152
Prob(F-statistic)
0.000000

Dependent Variable: Y
Method: Least Squares
Date: 12/20/09 Time: 22:09
Sample: 1974 1988
Included observations: 15
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
-80.15322
211.5083
-0.378960
0.7108
X3
0.068291
0.010294
6.634063
0.0000
R-squared
0.771973
Mean dependent var
1136.720
Adjusted R-squared
0.754432
S.D. dependent var
823.0463
S.E. of regression
407.8587
Akaike info criterion
14.98328
Sum squared resid
2162534.
Schwarz criterion
15.07769
Log likelihood
-110.3746
F-statistic
44.01080
Durbin-Watson stat
1.022370
Prob(F-statistic)
0.000016

Dependent Variable: Y
Method: Least Squares
Date: 12/20/09 Time: 22:10
Sample: 1974 1988
Included observations: 15
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
133.3664
117.5810
1.134251
0.2772
X4
0.012904
0.001209
10.67062
0.0000
R-squared
0.897526
Mean dependent var
1136.720
Adjusted R-squared
0.889644
S.D. dependent var
823.0463
S.E. of regression
273.4151
Akaike info criterion
14.18342
Sum squared resid
971825.5
Schwarz criterion
14.27783
Log likelihood
-104.3757
F-statistic
113.8620
Durbin-Watson stat
1.716793
Prob(F-statistic)
0.000000

Dependent Variable: Y
Method: Least Squares
Date: 12/20/09 Time: 22:10
Sample: 1974 1988
Included observations: 15
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
-194.0396
220.6236
-0.879505
0.3951
X5
0.637642
0.093473
6.821702
0.0000
R-squared
0.781643
Mean dependent var
1136.720
Adjusted R-squared
0.764847
S.D. dependent var
823.0463
S.E. of regression
399.1167
Akaike info criterion
14.93995
Sum squared resid
2070823.
Schwarz criterion
15.03436
Log likelihood
-110.0496
F-statistic
46.53562
Durbin-Watson stat
0.974820
Prob(F-statistic)
0.000012

Dependent Variable: Y
Method: Least Squares
Date: 12/20/09 Time: 22:11
Sample: 1974 1988
Included observations: 15
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
1482.477
2347.499
0.631514
0.5387
X6
-3.285416
22.20766
-0.147941
0.8847
R-squared
0.001681
Mean dependent var
1136.720
Adjusted R-squared
-0.075113
S.D. dependent var
823.0463
S.E. of regression
853.3975
Akaike info criterion
16.45989
Sum squared resid
9467734.
Schwarz criterion
16.55430
Log likelihood
-121.4492
F-statistic
0.021886
Durbin-Watson stat
0.215522
Prob(F-statistic)
0.884660

Dependent Variable: Y
Method: Least Squares
Date: 12/20/09 Time: 22:12
Sample: 1974 1988
Included observations: 15
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
1337.975
621.3416
2.153364
0.0506
X7
-25.42163
73.42366
-0.346232
0.7347
R-squared
0.009137
Mean dependent var
1136.720
Adjusted R-squared
-0.067083
S.D. dependent var
823.0463
S.E. of regression
850.2046
Akaike info criterion
16.45240
Sum squared resid
9397021.
Schwarz criterion
16.54680
Log likelihood
-121.3930
F-statistic
0.119877
Durbin-Watson stat
0.246059
Prob(F-statistic)
0.734708
从上述7个表可以看出，以X4为解释变量时，R2最大，但常数项不显著，就把不含常数项含X4的一元线性回归模型作为基本模型（所有不含常数项的一元线性回归模型中，此模型R2最大）
在此基础上分别加入X1,X2,X3,X5,X6,X7
Dependent Variable: Y
Method: Least Squares
Date: 12/20/09 Time: 22:21
Sample: 1974 1988
Included observations: 15
Variable
Coefficient
Std. Error
t-Statistic
Prob.
X4
0.010598
0.001061
9.988042
0.0000
X1
0.003000
0.000810
3.704267
0.0026
R-squared
0.945213
Mean dependent var
1136.720
Adjusted R-squared
0.940999
S.D. dependent var
823.0463
S.E. of regression
199.9192
Akaike info criterion
13.55727
Sum squared resid
519580.1
Schwarz criterion
13.65168
Log likelihood
-99.67952
F-statistic
224.2834
Durbin-Watson stat
1.190080
Prob(F-statistic)
0.000000

Dependent Variable: Y
Method: Least Squares
Date: 12/20/09 Time: 22:22
Sample: 1974 1988
Included observations: 15
Variable
Coefficient
Std. Error
t-Statistic
Prob.
X4
0.007698
0.002448
3.145342
0.0077
X2
0.016101
0.006054
2.659477
0.0197
R-squared
0.927066
Mean dependent var
1136.720
Adjusted R-squared
0.921456
S.D. dependent var
823.0463
S.E. of regression
230.6650
Akaike info criterion
13.84338
Sum squared resid
691682.2
Schwarz criterion
13.93778
Log likelihood
-101.8253
F-statistic
165.2434
Durbin-Watson stat
1.886847
Prob(F-statistic)
0.000000

Dependent Variable: Y
Method: Least Squares
Date: 12/20/09 Time: 22:26
Sample: 1974 1988
Included observations: 15
Variable
Coefficient
Std. Error
t-Statistic
Prob.
X4
0.011413
0.002914
3.916365
0.0018
X3
0.012656
0.013791
0.917717
0.3755
R-squared
0.894237
Mean dependent var
1136.720
Adjusted R-squared
0.886102
S.D. dependent var
823.0463
S.E. of regression
277.7686
Akaike info criterion
14.21502
Sum squared resid
1003020.
Schwarz criterion
14.30943
Log likelihood
-104.6126
F-statistic
109.9165
Durbin-Watson stat
1.648368
Prob(F-statistic)
0.000000

Dependent Variable: Y
Method: Least Squares
Date: 12/20/09 Time: 22:27
Sample: 1974 1988
Included observations: 15
Variable
Coefficient
Std. Error
t-Statistic
Prob.
X4
0.010146
0.002249
4.511236
0.0006
X5
0.166624
0.092648
1.798469
0.0954
R-squared
0.909822
Mean dependent var
1136.720
Adjusted R-squared
0.902885
S.D. dependent var
823.0463
S.E. of regression
256.4876
Akaike info criterion
14.05560
Sum squared resid
855216.8
Schwarz criterion
14.15001
Log likelihood
-103.4170
F-statistic
131.1597
Durbin-Watson stat
1.546147
Prob(F-statistic)
0.000000

Dependent Variable: Y
Method: Least Squares
Date: 12/20/09 Time: 22:28
Sample: 1974 1988
Included observations: 15
Variable
Coefficient
Std. Error
t-Statistic
Prob.
X4
0.012874
0.001180
10.91316
0.0000
X6
1.310060
1.085108
1.207309
0.2488
R-squared
0.898739
Mean dependent var
1136.720
Adjusted R-squared
0.890950
S.D. dependent var
823.0463
S.E. of regression
271.7927
Akaike info criterion
14.17152
Sum squared resid
960326.4
Schwarz criterion
14.26593
Log likelihood
-104.2864
F-statistic
115.3811
Durbin-Watson stat
1.726650
Prob(F-statistic)
0.000000

Dependent Variable: Y
Method: Least Squares
Date: 12/20/09 Time: 22:28
Sample: 1974 1988
Included observations: 15
Variable
Coefficient
Std. Error
t-Statistic
Prob.
X4
0.013930
0.001168
11.92717
0.0000
X7
1.062945
13.41974
0.079208
0.9381
R-squared
0.887440
Mean dependent var
1136.720
Adjusted R-squared
0.878781
S.D. dependent var
823.0463
S.E. of regression
286.5559
Akaike info criterion
14.27731
Sum squared resid
1067486.
Schwarz criterion
14.37172
Log likelihood
-105.0798
F-statistic
102.4936
Durbin-Watson stat
1.705970
Prob(F-statistic)
0.000000

以X4、X1为解释变量的模型为基本回归模型，在此基础上分别加入x2、x3、x5、x6、x7得
Dependent Variable: Y
Method: Least Squares
Date: 12/20/09 Time: 22:33
Sample: 1974 1988
Included observations: 15
Variable
Coefficient
Std. Error
t-Statistic
Prob.
X4
0.005266
0.001540
3.420007
0.0051
X1
0.002776
0.000560
4.956802
0.0003
X2
0.014272
0.003628
3.933280
0.0020
R-squared
0.976068
Mean dependent var
1136.720
Adjusted R-squared
0.972079
S.D. dependent var
823.0463
S.E. of regression
137.5281
Akaike info criterion
12.86239
Sum squared resid
226967.8
Schwarz criterion
13.00400
Log likelihood
-93.46793
F-statistic
244.7054
Durbin-Watson stat
1.836293
Prob(F-statistic)
0.000000

Dependent Variable: Y
Method: Least Squares
Date: 12/20/09 Time: 22:34
Sample: 1974 1988
Included observations: 15
Variable
Coefficient
Std. Error
t-Statistic
Prob.
X4
0.005903
0.002129
2.772642
0.0169
X1
0.003349
0.000704
4.755746
0.0005
X3
0.021025
0.008633
2.435613
0.0314
R-squared
0.963337
Mean dependent var
1136.720
Adjusted R-squared
0.957227
S.D. dependent var
823.0463
S.E. of regression
170.2195
Akaike info criterion
13.28891
Sum squared resid
347696.2
Schwarz criterion
13.43052
Log likelihood
-96.66683
F-statistic
157.6545
Durbin-Watson stat
1.544291
Prob(F-statistic)
0.000000

Dependent Variable: Y
Method: Least Squares
Date: 12/20/09 Time: 22:34
Sample: 1974 1988
Included observations: 15
Variable
Coefficient
Std. Error
t-Statistic
Prob.
X4
0.006579
0.001560
4.218358
0.0012
X1
0.003037
0.000633
4.795687
0.0004
X5
0.171886
0.056476
3.043539
0.0102
R-squared
0.969081
Mean dependent var
1136.720
Adjusted R-squared
0.963927
S.D. dependent var
823.0463
S.E. of regression
156.3193
Akaike info criterion
13.11854
Sum squared resid
293228.8
Schwarz criterion
13.26015
Log likelihood
-95.38901
F-statistic
188.0534
Durbin-Watson stat
1.625470
Prob(F-statistic)
0.000000

Dependent Variable: Y
Method: Least Squares
Date: 12/20/09 Time: 22:36
Sample: 1974 1988
Included observations: 15
Variable
Coefficient
Std. Error
t-Statistic
Prob.
X4
0.009426
0.001168
8.066916
0.0000
X1
0.003015
0.000746
4.043794
0.0016
X6
1.342893
0.734814
1.827529
0.0926
R-squared
0.957142
Mean dependent var
1136.720
Adjusted R-squared
0.949999
S.D. dependent var
823.0463
S.E. of regression
184.0414
Akaike info criterion
13.44505
Sum squared resid
406454.9
Schwarz criterion
13.58667
Log likelihood
-97.83791
F-statistic
133.9960
Durbin-Watson stat
1.251355
Prob(F-statistic)
0.000000

Dependent Variable: Y
Method: Least Squares
Date: 12/20/09 Time: 22:36
Sample: 1974 1988
Included observations: 15
Variable
Coefficient
Std. Error
t-Statistic
Prob.
X4
0.009792
0.001359
7.202709
0.0000
X1
0.003175
0.000833
3.810695
0.0025
X7
9.184487
9.634142
0.953327
0.3592
R-squared
0.949070
Mean dependent var
1136.720
Adjusted R-squared
0.940582
S.D. dependent var
823.0463
S.E. of regression
200.6240
Akaike info criterion
13.61760
Sum squared resid
482999.7
Schwarz criterion
13.75921
Log likelihood
-99.13199
F-statistic
111.8097
Durbin-Watson stat
1.285437
Prob(F-statistic)
0.000000

以X1 、X2 、X4为解释变量的模型为基本模型，在此基础上再加入 X3、X5、X6、X7
Dependent Variable: Y
Method: Least Squares
Date: 12/20/09 Time: 22:44
Sample: 1974 1988
Included observations: 15
Variable
Coefficient
Std. Error
t-Statistic
Prob.
X4
0.006048
0.001718
3.520635
0.0048
X1
0.002410
0.000664
3.627167
0.0040
X2
0.021343
0.007822
2.728540
0.0196
X3
-0.015337
0.015036
-1.020005
0.3296
R-squared
0.978136
Mean dependent var
1136.720
Adjusted R-squared
0.972172
S.D. dependent var
823.0463
S.E. of regression
137.2971
Akaike info criterion
12.90535
Sum squared resid
207355.5
Schwarz criterion
13.09416
Log likelihood
-92.79013
F-statistic
164.0331
Durbin-Watson stat
1.825783
Prob(F-statistic)
0.000000
Dependent Variable: Y
Method: Least Squares
Date: 12/20/09 Time: 22:45
Sample: 1974 1988
Included observations: 15
Variable
Coefficient
Std. Error
t-Statistic
Prob.
X4
0.005132
0.001588
3.232480
0.0080
X1
0.002835
0.000579
4.891619
0.0005
X2
0.011266
0.005773
1.951498
0.0769
X5
0.053741
0.079056
0.679778
0.5107
R-squared
0.977032
Mean dependent var
1136.720
Adjusted R-squared
0.970768
S.D. dependent var
823.0463
S.E. of regression
140.7181
Akaike info criterion
12.95457
Sum squared resid
217817.5
Schwarz criterion
13.14339
Log likelihood
-93.15930
F-statistic
155.9783
Durbin-Watson stat
1.855979
Prob(F-statistic)
0.000000

Dependent Variable: Y
Method: Least Squares
Date: 12/20/09 Time: 22:46
Sample: 1974 1988