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1、第八周作业ARCH和GARCH模型的估计实验内容及要求实验内容：以上证A股指数为研究对象，以所给数据为样本，对其收益率的波动性进行研究实验步骤：1、描述性统计(1) 建立工作文件，并导入数据。(2) 生成收益率的数据列在Eviews窗口主菜单栏下的命令窗口中键入如下命令：genr pr=log(p/p(-1)，回车 后即形成收益率的数据序列，或者键入如下命令：genr pr= p/p(-1)-1，回车后即形成收 益率的数据序列pr。(3) 观察收益率的描述性统计量给出描述统计量的图形，并进行相应分析。观察其时序图，可以看到波动集群现象，大的波动后波动大，小的波动后波动小，成团 出现。SPR-1
2、Q| I匕5010015020325030Q3S0 圳 0牯 0500lean Lie di an blaximum Minimum Std. De. Skewness Kurtosls观察其直方图与描述性统计量，其分布异于正态分布。进行Jarque-Bera检验，其伴随 概率为0，拒绝该分布是正态分布的原假设，因此待检验序列不符合正态分布。Series: SPR Sample 1 500 Observations 4990.0024740.0020410.133140-0.0972410.0324630.294307+.251243Jarque-Bera S9.75527Probabilit
3、y 0.0000002、对收益率序列进行平稳性检验给出平稳性检验的结果，并给出相应结论。对收益率序列进行单位根检验，模型3与模型2的伴随概率为0，拒绝有单位根的原假 设，说明序列是平稳的。但模型3的时间趋势项的伴随概率为0.1895，常数项的伴随概率0.7314,在显著性水平0.05情况下不显著，故不选用。而模型2的常数项的伴随概率为0.1121, 也不显著，不选用。因此模型1是最合适的模型，不含有常数项和时间趋势项。Null Hypothesis SPRhas i_rrt realEkdehdus Conslml； Urear Trend .agLcnalh ) I加OTTHtic - tJ
4、Etl Ofl SIC, mdDg=17)t-SlafisbcPre*/Auflmerced&ck&-F uler is 或 alMsnc-23 589900 DfflDTesl criliEai values1% kvd-3976591-34I897010%淑-3131976MacKinnon i 邙明 mnewiled相果律NUI Hyputhe攵冬 5FR ha& a uni rootEscgenaLK： ConstantLeg Length： 0 (Autaimabc - b35Ki on SIC, rnas(iag=17)t-Stafisik Prefa1加manted CkKe、*
5、ulr 脂st-205S31。Q POOPTea crceal ualues1 蠢巨陌-14432E45%kw;l-2 9&7124iOtevBi-25$9806MacKimon (19GGJ nne-sided p-/duesigmertEd OckCf-F uler Teal EquationCcpmd Pt varietjlc： D(SPftJMeltiod: L&eer SquaresDale O5W2O ima: 19:22mam欧仅M&Ledi 3 5CHIrcbdBl otealcms 498 afttr- adiusn errtsVai a t4eCoeffic-itnlSid
6、 ErrorPrabSPR(-1-09225740 044S07皿抻知O.OGOOC-Q001M10(HKgi63+34670.T314TRENEXT1.33E-O51.01E-D51.313&330.1995R-squBred&4IM3Meisn dependErt yar2 0J5航面R R-sqiJLXWl045fr187SC（泌。卸L河D.044KBS.E nF rpgnesEinnD032378视岫 irfn crrlpnan-4 016610Sum 钩wared rasni0.5HBSM1Skherz crilerwn-91275L眺i li心EM1033.13Hdrinanumn
7、cnKT.-4.OJ5635F-5alislie211 9760Durtiln-Vion 宝aL2 MamPrab!F-si3h5tE|ttOOKOaAugmented CickHy-Fuler Ti Equation Epenckirtt ”H3曲 DI.SPR) hlettiod Least S口u*乾 Cate DaiDai2d Toe 1S:22 Sanpk; i：丽林1： 3 500 hcliKtefli obstirvjbons 498 after adjusirnerTtsCoefficientSid Emir 1-StalBbcPnab.S河1-D-91B5E0DD44T33
8、-20.5331 QQ.OCHBCQiMMIISlDAO14501.59IH33a 1121R-squared0-+5&4&4hie an ctepeidentvar20&E wn |011 n-nui oas iU3fU 0 013 rvcn.i o-oia u-uia a-oa? Da OCJIfl i cr? 0-003 O 口S 0-015 !网 OOD4 -1U3 0 041 rt n-i-d ai3 -U-CJ1 1 作凸w ooe-7IF Cl 1H a-oja DO&2 陆DEIr.lhr.:d.7HdpdH 、=.ll72ilnITJ rs!?.二.qy rl-Bir芸寓密弱
9、密瞻碧拶电富普备圈担ss嵩脂U口口PI3口DDn口uclnduCIDPllCIDcilz 口 DDnDUDDDn-UDn.11 Ir K M40G u D h : a- r I 1 B 1 ft N ,.!0. .-?矿 1-dN H li捋LMJr1 llM lJH 1 N4X1 4HJI1 H M.Ha A-arTRHadMDD-H-Rn qH-0 a-sd fl .qDs-Rmfii-GTrFF./* psr2a:zEi244d.44-4Tcl11111 ? 了 X ? N Hr4113JiM- 1 53g NDHr-Hri; To:-.rlGi!tll!7,Nf1r1Ll-T 1 rl
10、rld 1X73 1WC-NI.-.-Je-Jm 财雄sws特佃湍 R%y:.2ssl5fl岩脖“岩 mvooclElQoo口aucl口 u-a o 0 n a o on a con a 00 o o A.(2)对收益率做自回归给均值方程回归的结果AR (1)：该模型各项显著，故对其进行残差项白噪声检验，观察Q检验及其伴随概率， 在显著性水平为0.05时，接受没有自相关性的原假设，是白噪声序列，可以选用。AC PAC Q-SI3I Prnbepaident兮PRMelEd ARI-W M3iniurnL*wlhaQd I6FGS)QalE D&I&20 Tin* 1705Sarrle: 2 5
11、00Incbdi ofeservstKing：药钮CanvEfgenc.e ach&eil an&-司 lia aicnsCaefficient coranance campited using outer producl G ywjhcrtsVarblsCosl Eiert：Sid ErrorLSta回IrPrahAR1)0.0369130.0371052.33&6440.01 &7SIGMASCIa OT1Q50523E-0520071154a OOMR squaredQ.O117B3Mean dedent varQ.D02474Adjjsted R-squareda 000226S D
12、dependml0 K34J33S.E negresEJnn0.03246Aka炽 hfo erfcarion-.013215SurnsQuarl 整邹10.523367Schwarz croerian-3SMS31Lnq ikdhDod1 Ml 257Hmncn-Quiin criterOjrtuh-Aatscn 汩12.013671Irrrted AR Roots.09ii|i1 -U(H2ii12 0 06Bi1I3。花i11I4却4i1l|16i1!16 0024ii!7 Q04Bi1i|iB -Q02Di1lI9 0觥iIIII10 0016i1l111i11I12 -0016i1l
13、|I13 Q013i1iI14- 0 014i1iI15 D-CK15i1116川舶Si1!II17 019i1I|I16 011i1iI1& QO25iii|I20 QCK31i1iI21 OQQ4i11122 0.013i11I!23 O.OSOi1l|124 -0034i1126 -0026111126 -fl.WDi1i127 0 016i11II26 &12i1l|129 -0.014i11|l30 0&221f1，31 Q05BiJiP32 QG73iil|i33 00iHll34。缩il36 &.O93iVl36 0065J3.O12 QjJ60 0.07A 0.062 -0.0
14、08 0.0W QQ溯 41.025 0.051 0.01S 0.Q12 尊也 43.001 0.G12 0.QO& 0.0S2 0.020 -0.004 g.oii 41.016 0.001 0.00& g2 -0.002 -0.044 胡.顾 0.015 0.02*-O.OOS o.ow Q顾 g.060 JO.OOl u.tm 0.Q74 0.06&0 0716 24136 D 5.3182 0 7.3627 0 7.3E28 0. 7.0EM9 0 3758 0 9 9596 D 10B91 0 1DS60 D 1L前 0. 11.179 0 11 262 0 11 360 D 11
15、372 D 1S.132 015- 325 0. 15 3S3 0 15.720 0 1&720 D15 7213 D 15.810 016- 250 0.16 257 016 675 0 17.M7 017 D 175 D 1LB35 0.18 085 0 19.911 0 22.7167 0 22 737 DD o 1 7 4 B 6 D -b 4 R- 7 1 7 2 1 8 2 & 3 O 3 4 2 3 B 2 o 9 7 C -120708111713顼222s3343&05als 心印561w07a闵网00昉囹DiSGMw明囹2S 24S DB96 2E-95G 0.?9B 29
16、 301 0 739Autocorr?nainnPETtial Corr珈顷4. ARCH效应的检验(1)用Ljung-Box Q统计量对均值方程拟和后的残差及残差平方做自相关检验:给出检验结果，并作相应结论。观察残差平方的自相关性，从伴随概率可见，其有很强的自相关性，说明存在ARCH 效 应。再进行ARCH效应检验。AjulwcrreifflcnPartial GorneiajonAC PACa-simProbibibi0 13& HIM土1汕0 002ii20 1511 0.13530.631DMAiiin3O DTD 0 03523.079DiMDi2i40 13D a.i&i31.56
17、0DM01fili50 056 0.01933.363QCWO*IIil150 016 -0 02333.430DM01II1I70 032 O.(M4做时OMO111II80 050 0 032352351)硕i1ii9HO够 0 i：ii：ha5.572DMOiHic0 0 梏 029皈6590-MOiliii110 0211 0.01615.877DM0iHIU130 035 0 0373B SMDoaniIIIi130 0211 o.mM747DiMDlr1F140.Q6D 0.Q&530.591o.oaoJii1*150fl3D 0.01039.042DW1liil1160 004
18、4.00039.0510 0011i(I17电 03? q 0S139 783QM1i11:!舟 003 -fl 1)0339.7670CO2HiHiI9q 翊 O. Mfi40 227DM3IiiO flTB O OB943.173DC02HiHi21JUMB。皿143.MDQQ31iII1220叩9刀D2443.399D0Q4iiii230M5 0D1241404DOMiH124O.Q25 -0.03543.735Q.OOBiliiI1250.(M044.233DQ1Qi1li25。睥 0 02444 43fl0 01*1111I2?a2Letbi SquaresCEeTime: ” 招S
19、EipF.gUSlEh 3 500InckKied observe*ons:耳岭 M机 EwluslrnftsCoeflicientStdl-StalislicPrab.C0.00090S99E-0&9 418 棉 9O&OOflREatpat-i) 13S37Domwgs 3J4238SOOC25R-quangd1O1B32OMean dependant flir0001051KinM利1 R-SQudJ&dQ.O1&34O3.D.判erWerM.伯“Oft 何 98S E d1陷g舶弦吧HDOD1903Akake infa crceran7K1E6Sun sci.iarMi nwd0.00
20、1758Schurz crternn-0.0&1271Slog iiMiwd2419-336Hgrngn-Quinn enter-9701549F-SflbSDC3 25B12SDirbin-iYalson 曳2036353PrnbJF-dattsiic)D 002471HeterosfcH招口和 Tesl： ARCHF-slfffes11cObeR-sqiared4B3D73D23.29750Frob F(6 4flB)Rnob 58钮如(5)0.0003OWXBTeaEquerliofl：Cepeidenl 7anable R9*klefl-icd Lead SqimsDate MJU01
21、2O Tme 1743Sami：teaii |LslEti：i: 7 6Q0ltdutted ofajirvalens 494 毗er adjuslrnenlsanaNeCoeffKIEfTlSid Error l-StaloiicProb.GODOIHT5OW01205M9569DOOMRSC*-1J0 105699 Sa 北 2 M9029口 口1卯fl十5的M折理OC453052 6775fifl00102FtESJP-S0021324OC4W01 0 475230&403RESIDE 4J0岫 IE；OG462992139921a 0291RESIDE 句OJMB247DW的0 431
22、1 a06724R-squarwi4JH7161Mabh depended var翊 ustaj R-suared0037396Si deperdEnl war0眄奶5 E i： r呵削 m0001069inftjeMebon9 7153J3Sum mqusE ud&顷m *SeLoq kliEhhDDd2405 flfifiHzrnan-Cum erter9舶典F-BiBlEUc4B30730OurbifvVisson 引徵1 95EH95Pro&CF-scatisdc)00M254Helerosteclllc Test ARCHHeleroskedastjcriy Test ARCHF-s
23、tatisticObsR-squarEd3.4X95923 由955Prob. F(8,482)Prob- Chi-Square(S)0.0023D DQ2BTest Equation:Dependent Vanable RESIDrt2Method Least SquaresDate- OS-USO Time: 17:4BSample adjusted): 10 500Included obsepyahons -4&1 after adjusimenisVariableCoefficientStd Error t-StatisdcProbc0 0D0663Q(TOD132 5.056618Q
24、OODQRESID*2(-1)010S75Q0 045S392.3222000 0206RESID*2( ?)0119115Q(H5e322 593916Q0096RESlCat-S)0.01&1400.M61540.4146990.6706RESIP2(-)0 097531Q04B1752.11122130 0352RESID*2(-5)0 01873200422904052070 6855RESID*2(-6)-0 0299890(M769 -0.6412150S217RESlD*2(-7)0.010109O.CM7540.216213O-02B9RESIE?2(-a)0032955Q04
25、B665 O7DG1S&0 48明R-squane0.046166Mean dependent var& 001063Adjusted R-squared0.032360S.D dependent var0.001909S E. of rEgression 0D1873Akaike info errterian-9 G993O2Sum squared resid0 001700Schwarz criteriDn-9 622381Log likelihood2390179Hannan-Qunn enter-9 669095F-statistic3.048S59Durbin-Watson stat
26、1.999346Prob(F-statistic)0 0D23454、GARCH类模型建分别给出残差为正态分布、T分布和广义误差分布的模型估计结果，并做相应分析。(是否 存在厚尾的情况？)(1) GARCH(1,1)模型估计结果正态分布：在方差方程中，各项都显著，进一步说明存在ARCH效应。均值方程各项不显著。DendefTlVariabt& SPRMelhod ML ARGH - Normal dlstrlbuljon (BFGS / Marquat sleci-E浏吠明向刖ND Time： 17：56Same (adjusled): 2 500included ofcsatens99 an
27、er adjuslmentsConveqjencB achieved aher 10 rierationsGucfliGicnl cavtsnanctr wmixrted usng auler product of 舟45$Pncsampk? vmancc: bac kceist (paMmet-cr = 0.7GARCH = CI2) 4 C(3)xRESID(-ir2 # C(4：iaGARGH(-1VeiriableCodficESW Errorz-SliiticPmKW(l)0.092171Q04 溺 B1.6772740 0605Variance EquationC0.000197B
28、.07E-053.00&9920.0020RESIEX-iyS0.2063-700.0513124.0213380.0OT1GWRCHM)0.&27&220.08-H287.4373840.0030R-sqjared0.001756Meai dependent 间0.002174Ar|usl&d Rquared0.001756S.Cl ilependenrt. var0.03263S_E. erf regression0.032434Akai rrfo crrtencti-4.0629011Sum aquared rsid0.523831Schibtfarz ertanan-4 Q4&132L
29、aq Ikihoad1022 34Hannan-Uunn crrler-4 069S49Durhn-WatEon 乖rt2.0242-41Inverled AR Rants.斓存在t分布：均值方程和方差方程各项都显著。观察t分布的自由度，为7.166035 3 0, 厚尾现象，与正态分布存在显著差异，说明投资者的投资行为并不是相互独立的。Dependent Variable SPRMeflicd ML 阴CH - Students I dralnbutiari (SFGS / Marwarct sep&|Dste:TmcHBOlSample (adjustedii 2 5D0IndixlKi
30、observeijons 499 fffter sdiuslrnerrtsCcnverpence achieved aHer 30 ieraioriaCDcfficitnt corrianct compitttl using oulrr prndud of g-eidirnlsFresample variance tatkeasi (praineiEr- = 0 7)GARCH 二 C(2) * G明ESIDl必* C(4rGAHCH(-1)VariaWeCdMOgeISid Errwz-StalistJCPrr*.0.0-77810CH80452 0352200.0419Variance E
31、quslcnG0.00013?6 67E-052 04896400*05RESID-HYZD 170655 口润的&2 BB227&o cog0711291101000927 10407口.0000T-CiST. OOF7.1660352 61262427*289口硕1R-squangdu.cm 做gan dependent -/ar0002474AjjjLfiied R-squarednOOIBbfiS.D dependerc uarD 032463SE ofneyesEion0.0324 酬版inlig entenon-4 109S56Sum squaiEd r酉id0.523&20Sch
32、rtarz cnlenon-4I366E4&Log ii树flood1030 160HcTin-Quirri enter-4晚澎DLfbn-VJasisn 顽x3.016144Hvfcrtad ar rmtIs.10广义误差分布：均值方程各项不显著，方差方程各项显著。广义误差系数为1. 4 90,在0到2之间，存在厚尾现象。同样说明投资者的投资行为并不是相互独立的。OEpendenl Variabte SPRMfflhoO ML WGH - GeiHrsfizeKl efror GSEinbuBoniCEC-i ipr：-1十EnableCoctfKIMTtStd Errorz-Still s
33、ticPrab.0.089436&.&4SZ711 8&W26OCB38Variarp：equalnnG RESI&M|2 GARO-K-1)0.0001610回物QHB13F73SE-050.063023n.1D7621822712 95M6S ft 19133500291Oijaaa omonGEDPARAJETER1 49920fl. 139802107267300000R-squared加j岫 R-squared dF regrtEHDn Sun squared rend LoglikeiihowiDurbh曲Is叩归a.wir?7 0. DOI 777 01)33414 0 5336
34、70 1020.610 2.G18445Mean dapentfenl m* sr- M阳膏Aka he info cnbefinn 3 匚 hifiarzcnlencri Hannan-QiJnn crtec0.W2474 0 03243 4.I02B45 4 00435 4JMD80Invaied AR RjoalsD9（2） GARCH-inMean 估计结果分别给出三种GARCH-inMean模型估计结果，并做相应分析。（是否存在风险溢价？）由于存在厚尾现象，因此不再考虑正态分布情况，基于T分布和广义误差分布进行分析。广义误差分布：1、引入方差：GARCH项和AR（1）项不显著，但无法说明不存在风险溢价，继续实验。Dependent Variable 5PRMethod Gaieralizei error diElnbutian (GED) BFGS iMarquardt steps)Dale 0M&2O Time. 19.13Sampleadjusted: 2 SODinclixted cteetvadcrs
