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 1.数据导入：2.对数收益率特征分析 3.（）简单描述性统计1（）平稳性检验2（）自相关性分析3（）损益的不对称性4（）分布的尖峰厚尾分析5（）波动聚集效应检验6对数收益率可预测性分析 4.（）短期1（）中期2（）长期3一、数据处理Lnrt=ln(1+rt*)其中为普通收益率rt*二、数据导入File—new—workfileDated-regular frequency; monthlyObject—new object—group—g1三、对数收益率特征分析（）简单描述性统计 1 table or stats&—histogram stats statisticslnrt窗口--view—descriptive&tests80LNRT Series:702014M091991M01Sample285Observations600.010218Mean50 0.006760Median 1.019664Maximum40-0.373282Minimum0.130937Dev.Std.302.438914Skewness21.00333Kurtosis204131.466Jarque-Bera100.000000Probability01.00.80.60.40.20.0-0.2-0.4．0.01021Mean0.00676Median1.01966Maximum-0.37328Minimum0.13093StdDev.2.43891Skewness21.0033Kurtosis4131.46Jarque-Bera0.00000Probability 2.91221Sum4.86901DevSuSq.28Observations gragh--line作图：view—LNRT1.21.00.80.60.40.20.0-0.2-0.4140002109804089294069612）平稳性检验（ADF-test 2nonelevel—View—unit root test—root unit LNRT Hypothesis:has aNull None Exogenous:maxlag=15)on SIC,basedLength:Lag0 (Automatic-Prob.*t-Statistic-17.52336statisticDickey-Fuller0.0000testAugmented levelTest1%-2.573130criticalvalues:level5%-1.941945level-1.61595310%p-values*MacKinnoone-side(1996EquatioTesAugmenteDickey-FullerD(LNRTVariableDependentSquareLeasMethod01:3TimeDate09/29/12014M01991M0Sampl(adjusted)adjustmentafteobservations28Include Errot-StatistiVariablCoefficienStdProb.0.05941-1.04108-17.52330.000LNRT(-1)va0.00013MeaR-squaredependen0.520394va0.18981dependen0.52039S.DAdjusteR-squaredcriterioinfregressioAkaik0.13145S.Eo-1.216828criteriosquareresi4.89016-1.20398SchwarSumcriter-1.21167Lolikeliho o173.789Hannan-Quinn1.99262Durbin-Watsostat）自相关性分析：（ACF&PACF336—level—correlogram—View（）损益不对称4作出分布图：view—gragh—distribution偏度：见（） 1 LNRT80706050yc n40eu qe30rF20100 1.2-0.20.00.8-0.40.20.41.00.6（）尖峰厚尾5见分布特征、偏度、峰度、及检验结果J-B（）波动率聚集6Genr vt=lnrt^2检验序列的自相关：ACF vt相关系数检验VT 1.21.00.80.60.40.20.0149206949610980800120204相关系数VT3VTVT2VT1 1.0000000.064741VT0.0498720.0542980.0647410.049843VT11.0000000.0646720.0498720.064714VT21.0000000.0646720.054298VT31.0000000.0647140.049843．收益率可预测性分析短期：、、、4132 ar(4)ar(3)ar(2)ls lnrt c ar(1)是一样的lnrt(-4)lnrt(-3)lnrt c lnrt(-1)与lslnrt(-2)LNRDependenVariable:SquareLeasMethod:01:5Date09/29/1Time2014M01991M0Sampl(adjusted):adjustmentobservations28afteIncludeiterationConvergencachieveafter ProbErroStdt-StatistiCoefficienVariable0.1720.010181.369380.0074370.427AR(1-0.047300.05949-0.795159vadependenR-square0.00223Mea0.01019 vadependen0.13116-0.00130S.DAdjusteR-squarecriterioAkaik0.13125S.Eo-1.21637regressioinf criterio-1.19067SusquareresiSchwar4.858053criterLolikelihoo-1.20607Hannan-Quin174.7252stat1.992328F-statistic0.632278Durbin-Watson 0.427190Prob(F-statistic)-.05Inverted AR Roots、、中期：12 96ar(12)ar(6)ar(9)ls lnrtcLNRTDependent Variable:Squares Method:Least01:57Time:Date:09/29/142014M091992M01(adjusted):Sampleadjustments observations:Included273after iterations3afterConvergence achievedProb.t-StatisticVariableErrorCoefficientStd.0.43250.0071490.0090960.786024C0.90350.121401AR(6)0.0587900.0071370.00050.0586040.205336AR(9)3.503772．0.221-0.07169-1.22435AR(120.0585590.00762vaMeadependenR-square0.048799LN DependentVariable0.13155dependenAdjusteR-squareva0.03819S.D R-1.24311criteriooregressioAkaik0.12902infS.E. SquaresLeast Method:-1.19023criterioresi4.47798SchwarSusquare09/29/14Date-1.22188173.685likelihoocriterHannan-QuinLog Time2.08214Durbin-WatsoF-statisti4.60011stat02:020.00370Prob(F-statistic.64+.58.74-.08A.64-.58Root.74+.08Inverte-.30+.68.18+.85-.30-.68.18-.85-.43+.60-.83-.27-.43 -.60-.83+.27LNRVariableDependenSquareMethodLeas02:0TimeDate09/29/12014M0(adjusted)1991M1SampladjustmentafteIncludeobservations27iterationConvergencachieveafteProbVariablErr oCoefficient-StatistiStd0.35430.0097650.0090600.927877C0.00063.4627680.203065AR(9)0.058642 vardependent0.0419270.009287MeanR-squaredvar0.1318340.038430S.D.AdjustedR-squared dependent criterion0.129276S.E.of-1.246511regressionAkaike info criterion-1.220276squaredSchwarz4.579180resid Sum criter.174.0185 Loglikelihood-1.235983Hannan-Quinnstat11.990762.055078F-statisticDurbin-Watson0.000620Prob(F-statistic).15+.82iAR.64-.54i.84Roots Inverted.64+.54i -.79+.29i.15-.82i-.42+.73i-.42-.73i-.79-.29i2014M09(adjusted):1992M01Sampleadjustments273afterIncluded observations:iterations after3Convergence achievedProb.VariableCoefficientStd.Errort-StatisticC0.50540.0098720.0065840.666927AR(1)-0.031776-0.5141170.0618060.6076AR(2)0.0610520.0180190.2951320.7681AR(3)0.0321530.0606200.5304010.5963AR(4)0.0834-0.1039040.059784-1.737983AR(5)0.059923-0.899022-0.0538730.3695AR(6)0.73750.3355750.0198530.059160AR(7)2.8078070.0589430.1655010.0054AR(8)-0.0002600.9965-0.0043470.059754AR(9)2.8045600.0594190.1666450.0054AR(10)0.0601560.1967-0.077865-1.294386AR(11)2.1491080.1296240.0603150.0325AR(12)-0.772824-0.0470200.44030.060841var Mean0.007626R-squared0.105523dependent var S.D.Adjusted R-squared0.1315590.064240dependent criterion Akaikeregression0.127263infoofS.E.-1.238670criterion4.210943-1.066790SchwarzresidSum squaredcriter.Hannan-Quinn182.0785Log-1.169674likelihood stat2.007225Durbin-Watson2.556064F-statistic 0.003269Prob(F-statistic)RootsAR Inverted.85.63+.57i.63-.57i.37-.14+.79i.27-.66i.27+.66i-.14-.79i-.87+.30i-.51-.68i-.51+.68i-.87-.30i长期：、、、64 244836ar(64)ar(36)ar(48)ar(24)lnrt c lsLNRTVariable:DependentSquaresMethod:Least01:59Time:Date:09/29/142014M09Sample(adjusted):1996M05adjustments221after Included observations:iterations3achievedConvergence afterProb.Variablet-Statistic CoefficientStd.Error0.1970.006271.293040.004850.0830.05118AR(24-0.08890-1.7370340.0501.96464AR(360.094900.048300.0760.037 90AR(48-1.78217-0.067550.374-0.89080-0.03291AR(640.03695vadependen0.005590.04883R-squareMeavadepend en0.03122AdjusteR-squareS.D0.08004criterioinfoS.E-2.22184regressio0.07878AkaikcriterioresiSusquare-2.14496Schwar1.34070criterHannan-Quin-2.19079Lolikelihoo250.513sta2.772471.84493Durbin-WatsoF-statisti0.02813Prob(F-statistic.94-.16.95+.05A.94+.16Root.95-.05Inverte.90-.21.90+.21.91+.33.91-.33.81-.49.86+.41.86-.41.81+.49.72+.63.75+.56.72-.63.75-.56.56-.75.56+.75.63+.72.63-.72.41-.86.49+.81.41+.86.49-.81.21-.90.33+.91.21+.90.33-.91.05+.95.05-.95.16+.94.16-.94-.16+.94-.16-.94-.05+.95-.05-.95-.33+.91-.21-.90-.21+.90-.33-.91-.49-.81-.49+.81-.41+.86-.41-.86-.63-.72-.56-.75-.63+.72-.56+.75-.75-.56-.72-.63-. 75+.56-.72+.63-.86-.41-.81-.49-.86+.41-.81+.49-.91+.33-.90-.21-.91-.33-.90+.21-.95-.05-.94+.16-.95+.05-.94-.16。