上证综指对数收益率月度数据的特征分析

1、上证综指对数收益率月度数据的特征分析（）1991.1-2014.9目录数据处理：收益率对数化数据导入：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FilenewworkfileDated-regular frequency; monthlyObject 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 -vie

2、w descriptivestatistics & tests histogram& stats or stats table80Series: LNRT7060Sample 1991M01 2014M09Observations 28550403020100-0.4-0.20.00.20.40.60.81.0Mean0.010218Median0.006760Maximum1.019664Minimum-0.373282Std. Dev.0.130937Skewness2.438914Kurtosis21.00333Jarque-Bera4131.466Probability0.000000

3、Mean0.010218Median0.006760Maximum1.019664Minimum-0.373282Std. Dev.0.130937Skewness2.438914Kurtosis21.00333Jarque-Bera4131.466Probability0.000000Sum2.912210Sum Sq. Dev.4.869011Observations285作图： view gragh-lineLNRT1.21.00.80.60.40.20.0-0.2-0.49294969800020406081012142）平稳性检验 ADF-testViewunit root test

4、 levelnoneNull Hypothesis: LNRT has a unit rootExogenous:NoneLag Length:0 (Automatic- based on SIC, maxlag=15)t-StatisticProb.*AugmentedDickey-Fullertest statistic-17.523360.0000Test criticalvalues:1%level-2.5731305%level-1.94194510% level-1.615953*MacKinnon(1996) one-sidedp-values.AugmentedDickey-F

5、uller Test EquationDependentVariable: D(LNRT)Method: LeastSquaresDate: 09/29/14Time: 01:34Sample(adjusted): 1991M02 2014M09Includedobservations:284 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.LNRT(-1)-1.0410890.059411-17.523360.0000R-squared0.520394Mean dependent var0.000137Adjuste

6、dR-squared0.520394S.D. dependentvar0.189813S.E. of regression0.131452Akaike info criterion-1.216828Sum squaredresid4.890168Schwarz criterion-1.203980Log likelihood173.7896Hannan-Quinncriter.-1.211677Durbin-Watsonstat1.9926203）自相关性分析： ACF&PACF Viewcorrelogram level36（4）损益不对称作出分布图： view graghdistribut

7、ion偏度：见（ 1）LNRT80706050ycne40uqerF3020100-0.4-0.20.00.20.40.60.81.01.25）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=lnrt2检验 vt 序列的自相关：ACF相关系数检验VT1.21.00.80.60.40.20.0929496980002040608101214相关系数VTVT1VT2VT3VT1.0000000.0647410.0498720.054298VT10.0647411.0000000.0646720.049843VT20.0498720.0646721.0000000.

8、064714VT30.0542980.0498430.0647141.000000收益率可预测性分析短期： 、2、3、41ls lnrt c ar(1) ar(2) ar(3)ar(4)与 lslnrt clnrt(-1)lnrt(-2) lnrt(-3) lnrt(-4)是一样的DependentVariable: LNRTMethod: Least SquaresDate: 09/29/14Time: 01:55Sample(adjusted):1991M02 2014M09Includedobservations:284 after adjustmentsConvergenceachie

9、vedafter 3 iterationsVariableCoefficientStd. Errort-StatisticProb.C0.0101840.0074371.3693870.1720AR(1)-0.0473080.059496-0.7951590.4272R-squared0.002237Mean dependent var0.010190AdjustedR-squared-0.001301S.D. dependentvar0.131167S.E. of regression0.131252Akaike info criterion-1.216375Sumsquaredresid4

10、.858053Schwarz criterion-1.190678Log likelihood174.7252Hannan-Quinncriter.-1.206072F-statistic0.632278Durbin-Watsonstat1.992328Prob(F-statistic)0.427190InvertedAR Roots-.05中期： 6、 9、12ls lnrt c ar(6) ar(9) ar(12)Dependent Variable: LNRTMethod: Least SquaresDate: 09/29/14Time: 01:57Sample(adjusted):19

11、92M01 2014M09Includedobservations:273 after adjustmentsConvergence achievedafter 3 iterationsVariableCoefficientStd. Errort-StatisticProb.C0.0071490.0090960.7860240.4325AR(6)0.0071370.0587900.1214010.9035AR(9)0.2053360.0586043.5037720.0005AR(12)-0.0716970.058559-1.2243580.2219R-squared0.048799Mean d

12、ependentvar0.007626Dependent Variable: LNAdjusted R-squared0.038191S.D. dependentvar0.131559RTS.E. of regression0.129022Akaike info criterion-1.243117Method: Least SquaresSum squared resid4.477986Schwarz criterion-1.190231Date: 09/29/14Log likelihood173.6855Hannan-Quinncriter.-1.221888Time:F-statist

13、ic4.600115Durbin-Watsonstat2.08214702:02Prob(F-statistic)0.003701Inverted AR Roots.74+.08i.74-.08i.64-.58i.64+.58i.18-.85i.18+.85i-.30-.68i-.30+.68i-.43+.60i-.43-.60i-.83+.27i-.83-.27iDependent Variable: LNRTMethod: Least SquaresDate: 09/29/14Time: 02:00Sample(adjusted): 1991M10 2014M09Includedobser

14、vations:276 after adjustmentsConvergenceachievedafter 3 iterationsVariableCoefficientStd. Errort-StatisticProb.C0.0090600.0097650.9278770.3543AR(9)0.2030650.0586423.4627680.0006R-squared0.041927Mean dependentvar0.009287AdjustedR-squared0.038430S.D. dependentvar0.131834S.E. of regression0.129276Akaik

15、e info criterion-1.246511Sum squaredresid4.579180Schwarz criterion-1.220276Log likelihood174.0185Hannan-Quinncriter.-1.235983F-statistic11.99076Durbin-Watsonstat2.055078Prob(F-statistic)0.000620InvertedAR Roots.84.64+.54i.64-.54i.15+.82i.15-.82i-.42-.73i-.42+.73i-.79+.29i-.79-.29iSample(adjusted): 1

16、992M01 2014M09Includedobservations:273 after adjustmentsConvergenceachievedafter 3 iterationsVariableCoefficientStd. Errort-StatisticProb.C0.0065840.0098720.6669270.5054AR(1)-0.0317760.061806-0.5141170.6076AR(2)0.0180190.0610520.2951320.7681AR(3)0.0321530.0606200.5304010.5963AR(4)-0.1039040.059784-1

17、.7379830.0834AR(5)-0.0538730.059923-0.8990220.3695AR(6)0.0198530.0591600.3355750.7375AR(7)0.1655010.0589432.8078070.0054AR(8)-0.0002600.059754-0.0043470.9965AR(9)0.1666450.0594192.8045600.0054AR(10)-0.0778650.060156-1.2943860.1967AR(11)0.1296240.0603152.1491080.0325AR(12)-0.0470200.060841-0.7728240.

18、4403R-squared0.105523Mean dependentvar0.007626AdjustedR-squared0.064240S.D. dependentvar0.131559S.E. of regression0.127263Akaike info criterion-1.238670Sum squaredresid4.210943Schwarz criterion-1.066790Log likelihood182.0785Hannan-Quinncriter.-1.169674F-statistic2.556064Durbin-Watsonstat2.007225Prob

19、(F-statistic)0.003269InvertedAR 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、 64ls lnrt c ar(24) ar(36) ar(48) ar(64)DependentVariable: LNRTMethod: Least SquaresDate: 09/29/14Time: 01:59Sample (adjusted): 1996M05 2014M09Included obser

20、vations:221 after adjustmentsConvergenceachievedafter 3 iterationsVariableCoefficientStd. Errort-StatisticProb.C0.0062730.0048511.2930490.1974AR(24)-0.0889090.051185-1.7370340.0838AR(36)0.0949040.0483061.9646430.0507AR(48)-0.0675560.037906-1.7821720.0761AR(64)-0.0329190.036954-0.8908070.3740R-squared0.048835Mean dependentvar0.005599Adjusted R-squared0.031221S.D. dependentvar0.080044S.E. of regression0.078784Akaike info criterion-2.221842Sum squared resid1.340704Schwarz criterion-2