ARCH和GARCH模型建模實(shí)驗(yàn)報(bào)告

1、課程名稱計(jì)量經(jīng)濟(jì)學(xué)模擬實(shí)訓(xùn)實(shí)驗(yàn)項(xiàng)目名稱ARCH和GARC模型建模班級(jí)經(jīng)濟(jì)r 0902姓名盧梅香學(xué)號(hào)090110091學(xué)時(shí)32小組成員盧梅香湖南商學(xué)院模擬實(shí)驗(yàn)報(bào)告實(shí)驗(yàn)地點(diǎn)：E602時(shí)間:2012-4-20實(shí)驗(yàn)?zāi)康模和ㄟ^運(yùn)用ARCH和GARC模型建模，進(jìn)行相關(guān)的數(shù)據(jù)分析。實(shí)驗(yàn)步驟與內(nèi)容: 計(jì)算匯率波動(dòng)的回報(bào)率,Rt = log( R) -log( R)Hbl=log(jpy)-log(jpy(-1) 畫出回報(bào)率的趨勢(shì)圖，觀察是否存在ARC嫩應(yīng)。如果存在，以Rt對(duì)常數(shù)項(xiàng)進(jìn)行回歸,即：并利用LM統(tǒng)計(jì)量檢驗(yàn)隨機(jī)干擾項(xiàng)的方差是否呈現(xiàn)ARCH效應(yīng)?Hbl=log(jpy)-log(jpy(-1)得到下圖Wj

2、i ” | 專 | (Jb_j wtjMI H v I Fir Il 的mf II Li可看出方差有內(nèi)聚效應(yīng)，應(yīng)該存在 ARC效應(yīng)。構(gòu)建eq1:hbl c 得到下圖BT1CV2： - IEqniatxQii: £>Q 1Varhf 11b; 1111L_) £門轄."JlI !lt-jeci3£n .£rOC3Qua c k Oil®- m rm i_i wloiFTi tv ftrcicG： Db; sets FrLLt Kar(« | ratz-a | Estsi a" s |Far«：bt |

3、tbt; |Kc.z3CiAHCHTArit：F-siaii si ic52 .bl 196Probaj IrtjfaudDODOODhs*R- sq.flrsd07 07511prnt)dt)iirtv0 oocTmT EusliorrDe e n deni Vana-i le. RE5ly2Melhod. Leari S qusr昶0*i7D/l2 71m*10 43S« ip Er(.ju>l?di. 3JOffincluderl 葉iffiyvew l25 affirfirlji.slirfl FnripniniVariiL E：CtieflkipniSt j. trr

4、oi t-已giitin-rub.C5.15e.-0ti.01E-CE 1D7QXCDOLIQORf01247207n U茨F8F：S 623512nonooS-squ-ane 亡_ JG1I05Mean dependent 冋BJB5E-05如1 jsiti -squa-ed0 D6C44fST CDendfflti-Br000174S.t H gimio巾Q 3D01K-Akaikt ififc curtenon14.&3DUBun squimil r«Did4 07=16Ech 帕 “ ait Orion14 52316Loq IjkFlihoad1D3EE Clt-=

5、!-7 3ti- li 匚a? BngeDu:±i n-Wdtsor Mat1DJCOSE.Prob(F-&ti1i5iic) DDODOO由圖看出存在ARC嫩應(yīng) 對(duì)回報(bào)率序列進(jìn)行ARCH模型建模與估計(jì)，經(jīng)反復(fù)計(jì)算，滯后階選2;構(gòu)建eq2:hbl c 選ARCH模型建模與估計(jì) Arch2 GarchO得到下圖13 ELIt Edit Q-bjietsQuick 01 lHelpVi h | Frot £ bj s | Pr imt | Uuit | Fr»a工.| Es timptai | F ntra(:£ 11S上僅電五 |i dsDepen

6、dent Variable： HBLMethod: ML ARCHDate: 04/2M2 Time. 10.15Sampfe(»dju?led): 2 1427Included obsorvalionG. 1426 alter adjusting sndpoirHsConvergence ®chi疑ed12 ilrlignsCoefficientSid Errorz-StaiisticProb.cO.OOD3830 0002001 日350000.0664Variance EquationC4.66E4£1.74E-062B.755&7O.COCOAPC

7、Hfl)口 20 田 900 0241628 %関的口 coooARCH(2)0.1137140.D196B65.7822B6O.COCOR-squared<1.001700Meam dspendeni var4.16E-D6Adjusiled R-squared0.003914S.D. dependenl varODOE277S.E. of regression0.005293Akaike info crilerion83JJ00Sum squarad raid0.097788Schwarz crtleriori817238Log l ikeli hoodJB75.216Durbin-

8、Watson stt1 927290由于ARCH模型本身的局限性，我們對(duì)模型進(jìn)行GARCH(1,1擬合；得到構(gòu)建eq3:hbl c 對(duì)模型進(jìn)行 GARCH(1,1擬合,options 的收斂精度改為1000 0.001 下圖M EVitWii - I EgLLalxQU： E(i3 f£:lr 1 ljset'sHr: 73 dmck UiJm、iLdior- iL：LrTi. tw- Firkas. 0b wal.|FfLELtl"kriv I Fj 4 E二 Q| Es tJ Ata | For«i2 ut. | £l bt& |程韻

9、氐|7jnaaie. d£LklFlhod- ML-MC-Da：0.Time. IC.33呂amph 加眥山214?Tncludcd abs(f¥J!iiDn«' 1426 after adjuil ng mcinnifliqeica ach審辺詞刖27 it叭防書Coeffi: iBrriSr cl Ettflir-Siai ii£Pioh.c'000145H DD0196n7H177Tn酬廠E q”ticmc7.63E-Q71.75E-C7d. 3S1477OODQOARCH：1)a DoceD.0D661C0 37383?OOOQC

10、GARCH(1D 94238ED 10FFF4lil gl0 ODOO只召qu.：ji目止unniTOMtdgpondriL 曲4.1tit-06Adjusftd R-ujutiid-0 002260S.D dHipedointvDr 002773.E. of rsgriifionQ DDCiEE-Maikt mig critenan6 0Q993BSum uared th - dC 097E39SchwitJ ( riliMioh«37?176Log llkelihdiad491ES2E-Duibin-MVclsan stat1 930242檢驗(yàn)GARC擬合后模型的殘差項(xiàng)是否是正態(tài)

11、分布的（用q-q圖，分位數(shù)對(duì)分位數(shù)圖），女口 果是，說明GARC擬合是合理，否則繼續(xù)運(yùn)用其他 GARCH模型來擬合；®|x讀出殘差 Series: RE Torhfile: 11-1Yitif: Ftrai:s Dbjitds | FrLGl. | Ubji亡 |Fr 亡電工卍 | 注upl歸 gn工 |11 SiLal, | 上豪乞業(yè)七 | Lin*： | £1 址FE由圖看出模型不是正態(tài)分布 從q-q圖來看，殘差的尾部概率顯然要比標(biāo)準(zhǔn)正態(tài)要大得多，因此要嘗試用其他GARCH類模型對(duì)數(shù)據(jù)進(jìn)行擬合； 擬合GARCH-M（1,1模型，觀察輸出結(jié)果。發(fā)現(xiàn) 盲項(xiàng)沒有顯著性，因此沒

12、有必要用GARCH-M(1,1 模型;潔 ETiLfs - IEgnalxqh: Ed! fL_) EilefcJ£1.ErocaS,Ti3ck Ctt a Jis £ii*dor-Ti. tv- Frics. 0bFr iat Xu*ik | Fj «| Toy遼比| El譏訂耘sJ & |DependenlHtLMelhnd- ML-Cl-DM&CH仙隹 Time.iu.ySamp - |.jjuUudli. 2 142?kirtJd'd brrwiorf 147 nfer nrij ”1 % rndpoinHCowiqencs sch

13、 wed Fftei 33irtei«tion5C-ceffiEieni£td tnoiZ-£iailEll£Pioh.譏Cl他Q l1=66fc03?243ra旳96cn nnc jw r：=q-n呂m倍？別G2VddianiCQ EquationC7.00C-U7179EJJ7d 197224DODQOAPCH<1)n nECTFingnFFfrH阿忙0 oooo匸 3dZ62Jr 3DEG4Z141 EOEEn DOQDW-tquanQl0 000343 166-06Al ufed P-iqu>f*d-0 血？360S D ctapEn

14、dentvir 0062775 E of rigriffipri0 00t26?mig ertengn5 3&7251Sum squaffli- ra d0 D 腫 630Schwarz cirireriom呂 36079SLog likelihood4915 610F-tatfslIiEa i»7EBubiikW±«i slitli 932263JBlJO11,結(jié)果發(fā)現(xiàn)GARCH下面對(duì)序列進(jìn)行TARCH以合。在Threshold選項(xiàng)中設(shè)定滯后階數(shù)為 模型不存在新息沖擊的非對(duì)稱性，即不存在杠桿效應(yīng)；沖 EViem - £Equ&tian:

15、 EQ3 Tbkkfilet 11-1I I TlIa Edit Objacts Vii«vi Frees ck Dgliont Bfindaw HblpYktf If'rocs Objects IPr mt I JJwe I Freci e Es tin &.t e IP or*e c-ts 11SKes ids IDependent Variable: HBLMethod ML - ARCHDate: 040/12 Time: 11: DISafnple(adjusted). 2 1427Included observalions: 1426 after adju

16、sting endpoints 自亡hi曲mH aftr 35 ilralidnSCofflci$ntSid Errorz-StalislitProb.cO.DOD1150JM02D50 56D0540.5754Variance EquationC7.68E-D71.71E-D74.495335O.COCOARCH 0 0379510 0067135B575M 0000(RESID<J)*ARCH(1)0.D122B10D0B0B91.5102140.1290GARCH0 9J45150 006437146 73550X00R-squared0.0000 陽Mean dependent

17、var4 IGE-DfiAdjusled R-squared用.002393S.D. dependent var0 00B277S.E. of regressiDiTkOOOB209Akaike info cri1rion-6B892B4Sum squared resid0D9Z630Schwarz errtenon-6 670331Lag liklihocd4917.059Durbin-Walson sKat1 930419CT2 U 擬合EGARC模型。因?yàn)門ARCH模型的設(shè)定是假設(shè)對(duì)t的影響是二次的，過于的簡(jiǎn)單2且單一，應(yīng)用EGARC模型說明5對(duì)' 的影響是指數(shù)的，而不是二次的。

18、C(3)是顯著的, 說明存在非對(duì)稱的杠桿效應(yīng)；y? E¥ijl；v - I EgLLalxQit.: ECi3 luzkfil:L_) EilefcJ£1.Eroca9,i3 ck Ctt Jis £ii*doT-UMTi. tv- Frics. 0bFr iat Xu*ik | Fj «| Toy遼比| El譏訂耘sJ & |DependenlHtLMelhnd- ML-Cl-加& 伽隹 Time.I1:C2Samp - |.jjuUudli. 2 142?kirtJd'd brrwiorf 147 nfcr nrij ”1 %

19、 rndpoinHCowiqencii achwed Fftei 153 itsiahoniC-ceffiEieni£td tnoiZ-£iailEll£Pioh.c0 J0C163Q DM血0 41UEquationc-D 35133=. 051E阻心仙10 ODDOlRL5KSQ«|SARrt|1C 13&S6?D DlltflCID 2E23CDODQO4 02183ngnFJFF"-1-r：-noneEG ARCH (1)亦30三r 3D472T7血.烽伯n DOtnW-tquanQl-0 000215Mk-in 憶ponrhm

20、 u新i 166-06Al ufed P-iquimsii-0 DDXOOS D ctapindiHnvir 0062775 E of rigriffipri0 00t26?Miikt mig critenan5 389303Sum squaffli- ra d0 0&7643Schwti < rilion£ B7O93OLog likelihood4917.13Duibin-MVelsan stat1 331SARCH效應(yīng)進(jìn)一步用成分ARCH模型擬合，再觀察殘差是否還存在EViews - (Equation: EQ3 Torkfile: 11-1)3 I_ild El

21、it Objd-ctE： Vi nw Pr ocs ulck Qtieus Vlndbiv HalfYi 好 | Froc 三 | Dbj E»ct三 | Far j nt | 兇陽亡 | Fir whe | EsA Lmdlt： | Fer亡匚見三七 |雪 |KE mid三 |Dependent VriablB： HBLMethod ML-ARCHDate: 04/2M2 Time: 11:D3Sampl£i(adjuGld)： 2 1427Included observations' 1426 after adjusling endpointsCDEwergeiiice achieved after 16 itaration%CneffitienlStd Errorz-StatisticProb.cOOOD2B9D.0X1991 2999090.193BVariance EquationPemn: C6.E6E-051.03E-056.477427D.OOODPfiifti! |Q-C0.9926430.0D293432.9422D.QDOOPerm: ARCH-GARCH0.05)6500.0D64344.7637000.0000Tran. |ARCH-O|0.0926240.020i0514.619517D.0000T