上证综指对数收益率月度数据的特征分析.docx

上证综指对数收益率月度数据的特征分析
（1991.1-2014.9）

目录
1. 数据处理：收益率对数化
2. 数据导入：
3. 对数收益率特征分析
（1） 简单描述性统计
（2） 平稳性检验
（3） 自相关性分析
（4） 损益的不对称性
（5） 分布的尖峰厚尾分析
（6） 波动聚集效应检验
4. 对数收益率可预测性分析
（1） 短期
（2） 中期
（3） 长期

一、 数据处理
Lnrt=ln(1+rt*)
其中rt*为普通收益率

二、 数据导入
File—new—workfile
Dated-regular frequency; monthly
Object—new object—group—g1

三、 对数收益率特征分析
（1）简单描述性统计
lnrt窗口--view—descriptive statistics & tests—histogram & stats or stats table

 Mean
 0.010218
 Median
 0.006760
 Maximum
 1.019664
 Minimum
-0.373282
 Std. Dev.
 0.130937
 Skewness
 2.438914
 Kurtosis
 21.00333

 JarqueBera
 4131.466
 Probability
 0.000000

 Sum
 2.912210
 Sum Sq. Dev.
 4.869011

 Observations
 285
作图：view—gragh--line

（2）平稳性检验ADF-test
View—unit root test—level—none

Null Hypothesis: LNRT has a unit root

Exogenous: None

Lag Length: 0 (Automatic - based on SIC, maxlag=15)

t-Statistic
  Prob.*

Augmented Dickey-Fuller test statistic
-17.52336
 0.0000
Test critical values:
1% level

-2.573130

5% level

-1.941945

10% level

-1.615953

*MacKinnon (1996) one-sided p-values.

Augmented Dickey-Fuller Test Equation

Dependent Variable: D(LNRT)

Method: Least Squares

Date: 09/29/14 Time: 01:34

Sample (adjusted): 1991M02 2014M09

Included observations: 284 after adjustments

Variable
Coefficient
Std. Error
tStatistic
Prob.  

LNRT(-1)
-1.041089
0.059411
-17.52336
0.0000

R-squared
0.520394
    Mean dependent var
0.000137
Adjusted R-squared
0.520394
    S.D. dependent var
0.189813
S.E. of regression
0.131452
    Akaike info criterion
-1.216828
Sum squared resid
4.890168
    Schwarz criterion
-1.203980
Log likelihood
173.7896
    Hannan-Quinn criter.
-1.211677
Durbin-Watson stat
1.992620

（3）自相关性分析：ACF&PACF
View—correlogram—level—36

（4）损益不对称
作出分布图：view—gragh—distribution
偏度：见（1）

（5）尖峰厚尾
见分布特征、偏度、峰度、及J-B检验结果

（6）波动率聚集
Genr vt=lnrt^2
检验vt序列的自相关：ACF
相关系数检验

相关系数

VT
VT1
VT2
VT3
VT
 1.000000
 0.064741
 0.049872
 0.054298
VT1
 0.064741
 1.000000
 0.064672
 0.049843
VT2
 0.049872
 0.064672
 1.000000
 0.064714
VT3
 0.054298
 0.049843
 0.064714
 1.000000

收益率可预测性分析
短期：1、2、3、4
ls lnrt c ar(1) ar(2) ar(3) ar(4)
与ls lnrt c lnrt(-1) lnrt(-2) lnrt(-3) lnrt(-4) 是一样的

Dependent Variable: LNRT

Method: Least Squares

Date: 09/29/14 Time: 01:55

Sample (adjusted): 1991M02 2014M09

Included observations: 284 after adjustments

Convergence achieved after 3 iterations

Variable
Coefficient
Std. Error
t-Statistic
Prob.  

C
0.010184
0.007437
1.369387
0.1720
AR(1)
-0.047308
0.059496
-0.795159
0.4272

R-squared
0.002237
    Mean dependent var
0.010190
Adjusted R-squared
-0.001301
    S.D. dependent var
0.131167
S.E. of regression
0.131252
    Akaike info criterion
-1.216375
Sum squared resid
4.858053
    Schwarz criterion
-1.190678
Log likelihood
174.7252
    Hannan-Quinn criter.
-1.206072
F-statistic
0.632278
    Durbin-Watson stat
1.992328
Prob(F-statistic)
0.427190

Inverted AR Roots
     -.05

中期：6、9、12

ls lnrt c ar(6) ar(9) ar(12)

Dependent Variable: LNRT

Method: Least Squares

Date: 09/29/14 Time: 01:57

Sample (adjusted): 1992M01 2014M09

Included observations: 273 after adjustments

Convergence achieved after 3 iterations

Variable
Coefficient
Std. Error
t-Statistic
Prob.  

C
0.007149
0.009096
0.786024
0.4325
AR(6)
0.007137
0.058790
0.121401
0.9035
AR(9)
0.205336
0.058604
3.503772
0.0005
AR(12)
-0.071697
0.058559
-1.224358
0.2219

R-squared
0.048799
    Mean dependent var
0.007626
Adjusted R-squared
0.038191
    S.D. dependent var
0.131559
S.E. of regression
0.129022
    Akaike info criterion
-1.243117
Sum squared resid
4.477986
    Schwarz criterion
-1.190231
Log likelihood
173.6855
    Hannan-Quinn criter.
-1.221888
F-statistic
4.600115
    Durbin-Watson stat
2.082147
Prob(F-statistic)
0.003701

Inverted AR Roots
 .74+.08i
     .74-.08i
   .64-.58i
 .64+.58i

 .1885i
     .18+.85i
  -.30-.68i
-.30+.68i

-.43+.60i
    -.43-.60i
  -.83+.27i
-.83-.27i

Dependent Variable: LNRT

Method: Least Squares

Date: 09/29/14 Time: 02:00

Sample (adjusted): 1991M10 2014M09

Included observations: 276 after adjustments

Convergence achieved after 3 iterations

Variable
Coefficient
Std. Error
t-Statistic
Prob.  

C
0.009060
0.009765
0.927877
0.3543
AR(9)
0.203065
0.058642
3.462768
0.0006

R-squared
0.041927
    Mean dependent var
0.009287
Adjusted R-squared
0.038430
    S.D. dependent var
0.131834
S.E. of regression
0.129276
    Akaike info criterion
-1.246511
Sum squared resid
4.579180
    Schwarz criterion
-1.220276
Log likelihood
174.0185
    Hannan-Quinn criter.
-1.235983
F-statistic
11.99076
    Durbin-Watson stat
2.055078
Prob(F-statistic)
0.000620

Inverted AR Roots
      .84
     .64+.54i
   .64-.54i
 .15+.82i

 .15-.82i
    -.42-.73i
  -.42+.73i
-.79+.29i

-.79-.29i

Dependent Variable: LNRT

Method: Least Squares

Date: 09/29/14 Time: 02:02

Sample (adjusted): 1992M01 2014M09

Included observations: 273 after adjustments

Convergence achieved after 3 iterations

Variable
Coefficient
Std. Error
t-Statistic
Prob.  

C
0.006584
0.009872
0.666927
0.5054
AR(1)
-0.031776
0.061806
-0.514117
0.6076
AR(2)
0.018019
0.061052
0.295132
0.7681
AR(3)
0.032153
0.060620
0.530401
0.5963
AR(4)
-0.103904
0.059784
-1.737983
0.0834
AR(5)
-0.053873
0.059923
-0.899022
0.3695
AR(6)
0.019853
0.059160
0.335575
0.7375
AR(7)
0.165501
0.058943
2.807807
0.0054
AR(8)
-0.000260
0.059754
-0.004347
0.9965
AR(9)
0.166645
0.059419
2.804560
0.0054
AR(10)
-0.077865
0.060156
-1.294386
0.1967
AR(11)
0.129624
0.060315
2.149108
0.0325
AR(12)
-0.047020
0.060841
-0.772824
0.4403

R-squared
0.105523
    Mean dependent var
0.007626
Adjusted R-squared
0.064240
    S.D. dependent var
0.131559
S.E. of regression
0.127263
    Akaike info criterion
-1.238670
Sum squared resid
4.210943
    Schwarz criterion
-1.066790
Log likelihood
182.0785
    Hannan-Quinn criter.
-1.169674
F-statistic
2.556064

    Durbin-Watson stat
2.007225
Prob(F-statistic)
0.003269

Inverted AR Roots
      .85
     .63+.57i
   .63-.57i
      .37

 .27-.66i
     .27+.66i
  -.14-.79i
-.14+.79i

-.51-.68i
    -.51+.68i
  -.87-.30i
-.87+.30i

长期：24、36、48、64

ls lnrt c ar(24) ar(36) ar(48) ar(64)
Dependent Variable: LNRT

Method: Least Squares

Date: 09/29/14 Time: 01:59

Sample (adjusted): 1996M05 2014M09

Included observations: 221 after adjustments

Convergence achieved after 3 iterations

Variable
Coefficient
Std. Error
t-Statistic
Prob.  

C
0.006273
0.004851
1.293049
0.1974
AR(24)
-0.088909
0.051185
-1.737034
0.0838
AR(36)
0.094904
0.048306
1.964643
0.0507
AR(48)
-0.067556
0.037906
-1.782172
0.0761
AR(64)
-0.032919
0.036954
-0.890807
0.3740

R-squared
0.048835
    Mean dependent var
0.005599
Adjusted R-squared
0.031221
    S.D. dependent var
0.080044
S.E. of regression
0.078784
    Akaike info criterion
-2.221842
Sum squared resid
1.340704
    Schwarz criterion
-2.144961
Log likelihood
250.5136
    Hannan-Quinn criter.
-2.190799
F-statistic
2.772472
    Durbin-Watson stat
1.844930
Prob(F-statistic)
0.028132

Inverted AR Roots
 .95+.05i
     .95-.05i
   .94+.16i
 .94-.16i

 .91+.33i
     .91-.33i
   .90+.21i
 .90-.21i

 .86-.41i
     .86+.41i
   .81+.49i
 81-.49i

 .75-.56i
     .75+.56i
   .72-.63i
 .72+.63i

 .63-.72i
     .63+.72i
   .56+.75i
 .56-.75i

 .49-.81i
     .49+.81i
   .41+.86i
 .41-.86i

 .33-.91i
     .33+.91i
   .21+.90i
 .21-.90i

 .16+.94i
     .16-.94i
   .05-.95i
 .05+.95i

-.05-.95i
    -.05+.95i
  16-.94i
-.16+.94i

-.21+.90i
    -.21-.90i
  -.33-.91i
-.33+.91i

-.41-.86i
    -.41+.86i
  -.49+.81i
-.49-.81i

-.56-.75i
    -.56+.75i
  -.63+.72i
-.63-.72i

-.72+.63i
    -.72-.63i
  -.75+.56i
-.75-.56i

-.81+.49i
    -.81-.49i
  -.86+.41i
-.86-.41i

-.90+.21i
    -.90-.21i
  -.91-.33i
-.91+.33i

-.94-.16i
    -.94+.16i
  -.95+.05i
-.95-.05i