1102115110931118116811181085113511381135123513011283125012101135108510601102115111271226121712151250121012681402148615341567158517172002208620591250121012681402148615341567158517172002208620592425232621762121200020001850164017001925185018301850179017001700175017751925200019751940188918812000202419001750164916011625160916491640164016201590152614511424142413291199117912851349126512991373144014511376132512611199121912501274136514241420138513211235121513101319131912791481195621652125208718951840187418631836189421052159213120292270241126523294336036863593348236153963432843094336438243264009400040704200427844354772481249084857486547114640487749024884483349034963480446794810457142503850377533572946234219942420246427632993310827292525245721362272217521002068195519501969202517261579176817661621169216341750162015151508152515021374121211981107105210691050109811501126120011931058104310269809761000121012641150111711881100104010281113115413501722161615251403149715221550157515381650180019332219260625632433《應(yīng)用時(shí)間序列分析（第四版）》王燕編著中國(guó)人民大學(xué)出版社第四章習(xí)題71974年1月至1994年12月，某地胡椒價(jià)格數(shù)據(jù)如下：（21行*12列）1檢驗(yàn)序列的平穩(wěn)性（Stata語(yǔ)句）.dropB-T.generaten=_n.renameAprice.tssetntimevariable:n,1to252delta:1unit.tslineprice=>{price}的時(shí)序圖由時(shí)序圖觀測(cè)得price變化落差很大，該序列不平穩(wěn)。再看看自相關(guān)圖：???(Stata語(yǔ)句).acprice-CRrprosnoLLaleFDCD.UA010203040LagBartlett'sformulaforMA(q)95%confidencebands{price}的自相關(guān)圖短期（延遲階數(shù)為5期及5期以內(nèi)）來(lái)看，自相關(guān)系數(shù)拖尾；長(zhǎng)期來(lái)看，自相關(guān)系數(shù)緩慢地由正轉(zhuǎn)負(fù)，一直是下降趨勢(shì)。序列值之間長(zhǎng)期相關(guān)，該序列非平穩(wěn)序列。（Ps.平穩(wěn)時(shí)間序列具有短期自相關(guān)性。）結(jié)合之前的時(shí)序圖，發(fā)現(xiàn)該序列具有明顯的長(zhǎng)期趨勢(shì)。考慮到price是月度數(shù)據(jù)，因此覺(jué)得該序列很有可能還???????????存在季節(jié)效應(yīng)。2檢驗(yàn)序列的方差齊性原序列具有長(zhǎng)期趨勢(shì)，所以需要平穩(wěn)化。（Stata語(yǔ)句）.generateDp=D1.price.labelvariableDppprice"oe.tslineDpe=>firstdifferenceof先對(duì)原序列做一階差分:QUO1-｛Dp｝的時(shí)序圖（一階）差分后序列｛Dp｝的長(zhǎng)期趨勢(shì)不再明顯，平穩(wěn)化效果很好。再看看｛Dp｝的自相關(guān)圖:（Stata語(yǔ)句）qdfosno.^ae^pcoruA010203040LagBartlett'sformulaforMA(q)95%confidencebands｛Dp｝的自相關(guān)圖由圖可見，短期（5期）內(nèi)標(biāo)便衰減直逼零值，衰減速度非?？?，明顯具有短期自相關(guān)性。％在延遲1期以后，除了當(dāng)k=30時(shí)跳出過(guò)陰影范圍，其余全都落在2倍標(biāo)準(zhǔn)誤的范圍內(nèi)，圍繞著零值做很小幅（約土0.1）的波動(dòng)。因此，｛Dp｝是平穩(wěn)的時(shí)間序列。平穩(wěn)性檢驗(yàn)通過(guò)，看白噪聲檢驗(yàn)。自相關(guān)圖明顯顯示：宙力0，咬力0。因此，｛Dp｝非白噪聲序列，有信息待提取。預(yù)處理完畢，開始識(shí)別模型:QDfosno.LalerrocoTUA2-0111010203040LagQDfosno.LalerrocoTUA2-0111010203040Lagn_Dfosno.ta.eKrocoTuala.Trap1020Lag95%Confidencebands[se=1/sqrt(n)]3040{Dp}的偏自相關(guān)圖(1)不考慮季節(jié)效應(yīng)，先試ARIMA模型，再試疏系數(shù)模型。①ARIMA模型i認(rèn)為禰和虹都拖尾，嘗試ARMA(1,1)AEIIUlregresEion田ariaa-抵andotherd：Modelhodd.HModel3|by/if方n||HeiahtwHependentv：ii_lable:Dp.\|QIndepeiLiisritvariabl^E：~\SuppresscoastanttARIMAmodelspeciFication?AIINA(p,4q)speciEication：13Aatoregressiyeorder(.p)0；；Integrated(differeiLce)orderQ*Moving-averageorder(qj或者arimaDp,arima(1,0,1)Ps.同arimaprice,arima(1,1,1)結(jié)果I>pCoef.OPGStd.Etrr.zP>lZ1[gConf.Interval]Dto_conE5.09975414_1650^0350-71?-22.6(32632.86217AIJUlarLI-一1130S34Z?S70-uei*7821.SlSVdllmsLI..072433.13124930.55-.184811.323617/sioma145.63823.5530940L3?0.40413C.￡743152.￡021￡ajuji1a:2-252Munkar口Eabc=251Waldchi2{2}■14Laglikelilicod&^IGOG.465Prob>■ch±2一0.COOO參數(shù)顯著性檢驗(yàn)通不過(guò)ii認(rèn)為禰1階截尾，0kk拖尾，嘗試蛔(1)酮ari>a-AKI1A.AEIAK,andotherdModal.Md,■|JoJ己].3||壬Dependentvariable：Imiependentv：ii_iables：IISupTirassconst：mttAJLlMXmodtlEpecificitio^.,J*■AHWA(p,土電)specification：Au*tarazeivaord.arZEniegrated(differenceJarierHoving"averageorier(q)去掉截距項(xiàng)再試(Stata語(yǔ)句)arimaDp,noconstantarima(0,0,1)Ps.結(jié)果同arimaprice,noconstantarima(0,1,1)得到結(jié)果白噪聲檢驗(yàn)(Stata語(yǔ)句).predictehat1,residual.wnteftqehat1PortmanteautestforwhitenoisePortmanteau(Q)statistic=45.3466Prob&chi2(40)=0.2589evPs.m.wntestqehat1,lags(2).wntestqehat1,lags(6).wntestqehat1,lags(12)都通過(guò)了.wntestbehat1=>.estaticARHIAregression￡.~iTiip：2-252HumJou￡afohsWaldchiZ|1J-251■47.15Loglikelihood=-1607.717Prob>cluZ=u.uuuuDp.Coef.OPGStd_Err?zP>IzI[淚Conf.Interval]BP_cons5.27709512-0.42-19.31292^.UCC99AJU1A1113.LI..337111_04917?76.870-000.2413205.434101^/Eii3ioa146.35633.53735441-370-0001394233153.29截距項(xiàng)不顯著AR工MAregression如Coef.0PGStd.Err.P>|3|[95%Conf.Interval]皿SIDiElLl_.33*0741_0489113￡.510.000.2422096433S3E5Xsigma146419C3.50909141.730.000139J5419153.2913Samrile:2-252Niuiberofobs=251Waldchi2(1J=47.ISLaglUzelihood--1697.803ProL牛chi2-0.0000對(duì)｛Dp｝構(gòu)建MA（1）模型（無(wú)截距項(xiàng)）成功，對(duì)殘差項(xiàng)進(jìn)行白噪聲檢驗(yàn)CumulativePeriodogramWhite-NoiseTestCO4aoodooOtoCNOQoo0.0000.400.50FrequencyBartlett's(B)statistic=0.70Prob>B=0.7145通過(guò)了白噪聲檢驗(yàn)，但這個(gè)檢驗(yàn)的前提是同方差殘差項(xiàng)是白噪聲序列，計(jì)算AIC/BIC：llodclOhsllCm-illI11(luC-dclJdtAICETC"-251-1607.3092'\3219.fill322?.66S=>ii認(rèn)為禰拖尾，0kk1階截尾，嘗試ARARIHAregression(1)ARIHAregression-AKIUjARIAXjandother|Mold.幻|lUdd.3||bWi曰&IWCfihXjSBependeritvtcriable.Indepindentvariables.CSuppreseconstanttAEJMAnEpficificutiotn.(*JaKHTFIAd,q)specs￡lcatiqxi：1A,W0A.w0A.￥Autoregresslveorder(p)Integrated(differsnce)orderMoving-Avarh.gaoirdbr(q)Coat.OPGStd-Eirr.zg1m|【96*Conf.Int]Do_ccns5.10151914.382010.35foT?23-23-036733.28974arLI..35593^2.0411353H-53J=u.uuu.2141395.4377389/sigma145.C512a.41.41D.COOUQ.7554152.507Sanple:2-252lJuilLierafobs=251Waldahi2(1)=72.74Loglikelihood-K0G.559Prob:-cHi2-0.OODO去掉截距項(xiàng)再試截距項(xiàng)不顯著AEIHA.regression(Stata語(yǔ)句)Simple:2-252NiiiLLkerofobs=251WaldchiZ(1)=73.11Laglikelihood=-1696617ProL>chi2=0.0000.arimaDp,noconstantarima(1,0,0)(Stata語(yǔ)句)DpCoef.OPGStd.Err.zP>|3|[95%Conf.luterval]皿SIarLI..35(875(_04173663.550.000.275D734438C778/Ei?3iiia14572123.50517341.570.000138-B512152.5912對(duì)｛Dp｝構(gòu)建AR(1)模型(無(wú)截距項(xiàng))成功，對(duì)殘差項(xiàng)進(jìn)行白噪聲檢驗(yàn)白噪聲檢驗(yàn)(Stata語(yǔ)句).predictehat2,residual.wntestqehat2PortmanteautestforwhitenoiseePortmanteau(Q)statistic=m>chi2(40)=40.3516CumulativePeriodogramWhite-NoiseTestPr0.4547Ps.0.wntestqehat2,lags(2).wntestqehat2,lags(6).wntCstqehat2,lags(12)都通過(guò)了.wntestb.wntestqehat2PortmanteautestforwhitenoiseePortmanteau(Q)statistic=m>chi2(40)=40.3516CumulativePeriodogramWhite-NoiseTestPr0.4547Ps.0.wntestqehat2,lags(2).wntestqehat2,lags(6).wntCstqehat2,lags(12)都通過(guò)了.wntestbehat2QU1QDOOanoOtoaMOcoo0.0000.400.50FrequencyBartlett's(B)statistic=0.67Prob>B=0.7551因?yàn)榍笆?一年)內(nèi)宙和011明顯跳出了2倍標(biāo)準(zhǔn)誤范圍，所以確定ma(1),ar(1)，與上面①i對(duì)｛Dp｝擬合ARMA(1,1)的情況一致，已經(jīng)知道擬合不成了。(2)換季節(jié)模型，先試簡(jiǎn)單的加法模型，再試復(fù)雜的乘積模型。步差分后序列的自因?yàn)榭紤]了季節(jié)因子，這里是月度數(shù)據(jù)，所以要對(duì)一階差分后序列進(jìn)行12步差分。觀察12相關(guān)系數(shù)和偏自相關(guān)系數(shù)的性質(zhì)，嘗試擬合季節(jié)模型。=>.pacS12Dpfosnorta.eFDCO^Uala.Trap.generateg12Dp=S12.Dp.labelvariableS12Dp"12stepsofthedifference'步差分后序列的自嘗試擬合季節(jié)模型。=>.pacS12Dpfosnorta.eFDCO^Uala.Trap.generateg12Dp=S12.Dp.labelvariableS12Dp"12stepsofthedifference'0a.acS12Dp00Bartlett'sformulaforMA(q)95%confidencebands40od-oOMOQOOOMO-od-o-aoo-95%Confidencebands[se=1/sqrt(n)]{S12Dp}的偏自相關(guān)圖①加法季節(jié)模型i禰1階12階截尾%拖尾，結(jié)合疏系數(shù)模型，對(duì)序列｛S12Dp｝擬合MA(1,12)模型iiR拖尾虹1階12階(13階)截尾，結(jié)合疏系數(shù)模型，對(duì)序列｛S12Dp｝擬合AR(1,12)或AR(1,12,13)模型iii綜合考慮R和虹幾階截尾的性質(zhì)(哪幾期延遲期數(shù)對(duì)應(yīng)的相關(guān)系數(shù)特別明顯)，對(duì)序列｛S12Dp｝擬合ARIMA((1,12)(1,12))模型AEZMArncidilspecificationModwlAEZMArncidilspecificationModwl2Model3bv/if/inWeigtitsSE/RobustReportingMaximization.Dependentvai-1abls:IrLdeperLiientvariables：或者(Stata語(yǔ)句).arimaS12Dp,ma(1,12)=>AP.IIIAregressionHuiiiljerofobsWaldchiZ(2JLoglikelihood=-1551_408PrLoglikelihood=-1551_408SlEDpCoef.OPGStd.Err.z*9Z1[95%Conf.Interval]S12Dp_cons-.1631442.783658-0.06?953-5.6190145.292726MJfflmmLILIS..1366809-.9075633.0619103-0768C582.21-11.8100270-000.015339-1.058217.2580225-.7569091/8igmEl151.32446.334823.890-000138.9084163.7404去掉截距項(xiàng).arimaS12Dp,noconstantma(1,12)=>.predictehat3,residual.wntestqehat3PortmanteautestforwhitenoisePortmanteau(Q)statistic=62.1168Prob>chi2(40)=0.0141Q統(tǒng)計(jì)量的？值<a,拒絕原假設(shè)，認(rèn)為殘差列非純隨機(jī)，序列｛S12Dp｝中還有信息未提取完畢，建模失敗Iii對(duì)序列｛S12Dp｝擬合AR(1，12)或AR(1，12,13)模型.arimaS12Dp,noconstantar(1,12).predictehat4,residual(13missingvaluesgenerated).wntestqehat4PortmanteautestforwhitenoisePortmanteau(Q)statistic=68.0750Prob>chi2(40)=0.0037失敗I1ort-iLLiLtiteau.(QJstatistic=61-1895.arimaS12Dp,ar(1,12,13)在wntestq時(shí)也失敗了PEOb*J=00111iii對(duì)序列｛S12Dp｝擬合ARIMA((1,12)(1,12))模型Portmanteau(Q)■Statistic=32.1318.arimaS12Dp,noconstantar(1,12)ma(1,12)在wntestq時(shí)也失敗了Protl>chi2(40)=?-785SAP.IMAregressicuj.S12I：-PCoe￡.□PGStd_Err.zIzI[954Cont-Interval]maLI..13?9￡080618162.220027.0158031.258118LIZ.-.9070947.07C7165-11.820-000-1.057456-.7567332/siijrEiia151.33936.32728223.920-000138-53811C3.7406Samp1e:14-252MuiLLtierofobs=239Waldchi2(2)=167_45Loglikelihood=-1551_409Prob>chi2=0.0000序列｛S12Dp｝所具有的短期相關(guān)性和季節(jié)效應(yīng)用加法模型無(wú)法充分、有效提取，這兩者之間具有更復(fù)雜的關(guān)系，不妨假定為乘積關(guān)系，嘗試用乘積模型來(lái)擬合序列的發(fā)展。②乘法季節(jié)模型先考慮｛S12Dp｝的短期相關(guān)性。觀察12階以內(nèi)（包括12階）的自相關(guān)系數(shù)和偏自相關(guān)系數(shù)，兩者均拖尾，所以嘗試用ARMA（1，1）模型提取差分后序列的短期自相關(guān)信息。再考慮｛S12Dp｝的季節(jié)相關(guān)性（季節(jié)效應(yīng)本身還具有相關(guān)性）。觀察以12期為單位的自相關(guān)系數(shù)和偏自相關(guān)系數(shù)，前??????.者1階截尾，后者拖尾，所以用以12步為周期的ARMA（0,1）12即MA（1）12模型提取序列｛S12Dp^季節(jié)自相關(guān)信息。綜上所述，（對(duì)原序列）擬合模型：ARIMA（l,1,l）X（0,1,1扇歸—ARIULjA"RTAXjath&rd：Mod乩|血匝LW||血匝L3|[b”iHin]|臉曰心||瀏Hepindentv：=Lt_i=±ti]_e:IndepemleTLiialiies:S12B?vjS-OSuppress應(yīng)玷tanttcAJtZNAmodelspecificaticn1nA-utoregi-essiwecrierLpJ0Intepi：-=±tedlsdi￡±erencejorder1*Movln廠averagedriertq)

-.ARIVAjARMASf理do^herM<delModelZModel.3bv/if/inheights5mms-:<rL：=ilAILLHAspeciticitiqil?SATiIMACF..D,Q,S)specification0tAutpr如-[F；iQ*Iiityg3-ated(.ilifterenne)order1Mcivin廠averageorierj1ZSeaEOiL：=ill：=tgCS)I.arimaS12Dp,arima(1,0,1)sarima(0,0,1,12)ARIMAre^re5sionSample:14Sample:14-252Logliheliliood=-154A.517Numberofobs-=239Waldchi^O?=Probaclii2=0.AOOftSLEDp□PGStd.Err.SF；W1H1[35*Coni.Int-erval]SIZBp_COI1S52537322.25918Z-0.410.682-5.353883J.501942AKOarLI..3108391.129548C2.0_004_1169292.624150JiiiaLI.-.03U3316.1565357-0.IS0.847-.3412619.28019CSMUG112maLI.一一275.S477-0.頓fl.997-541.￡515539.^515/siiipiLa141_020519448.810.010.4970：J825?_9?截距項(xiàng)，參數(shù)有和參數(shù)％2均不顯著。季節(jié)效應(yīng)如此明顯的序列｛S12Dp｝居然難以構(gòu)建乘積季節(jié)模型。回到ARIMA模型:

由于對(duì)｛Dp｝構(gòu)建的MA（1）模型（無(wú)截距項(xiàng)）較好，觀察該模型的殘差圖和殘差平方圖（Stata語(yǔ)句）.tslineehat1=>□50100150200250nARIMA(0,1,1)(noconstant)的殘差圖1從殘差圖看，方差變化幅度較大，參差不齊。.twoway(connectedehatlnin1/252)=>050100150200250nARIMA(0，1，1)(noconstant)的殘差圖2.generatee12=ehat1*ehat1(1missingvaluegenerated)

.twoway(connectede12n)□50100150200250nARIMA(0,1,1)(noconstant)的殘差平方圖Ps.tslinee12也可以得到殘差平方圖(同均值的殘差序列的方差就是殘差平方的期望，)殘差平方圖上的異方差性太過(guò)明顯了。3考察序列的差分平穩(wěn)屬性，并考察過(guò)差分特征差分的目的是平穩(wěn)序列。過(guò)差分，過(guò)多次數(shù)的提取信息，雖然提取掉了非平穩(wěn)的確定性信息，卻浪費(fèi)了更多的其他信息。第2小題中，我對(duì)原序列進(jìn)行了1階12步差分，從時(shí)序圖和自相關(guān)圖可見，1階差分后序列｛Dp｝變平穩(wěn)了，如果再考慮季節(jié)因素，對(duì)｛Dp｝進(jìn)行12步差分，得到序列｛S12Dp｝，它的時(shí)序圖為：時(shí)序圖顯示，雖然序列｛S12Dp｝具有集群效應(yīng)，但從整個(gè)觀察期來(lái)看，多數(shù)時(shí)間序列波動(dòng)不大。自相關(guān)圖在第2小題里：

Oto-0102030Lag400—Bartlett'sformulaforMA(q)95%Oto-0102030Lag400—自相關(guān)圖顯示，短期內(nèi)延遲一階后序列｛S12Dp｝的自相關(guān)系數(shù)即落入陰影區(qū)域內(nèi)，之后，絕大部分滯后期的自相關(guān)系數(shù)也在陰影范圍內(nèi)。序列｛S12Dp｝短期自相關(guān)，比較平穩(wěn)。過(guò)差分的情況會(huì)是怎樣？在Stata中嘗試對(duì)序列｛Dp｝再做一次差分：（Stata語(yǔ)句）.generateD2p=D.Dp.tslineD2p.acD2p比照2階差分后序列比照2階差分后序列｛D2p｝與1階后序列｛Dp｝的時(shí)序圖、自相關(guān)圖：｛Dp｝的自相關(guān)圖｛D2p｝的自相關(guān)圖｛Dp｝的自相關(guān)圖｛D2p｝的自相關(guān)圖1AIf1oo??4TJtL■11III由時(shí)序圖發(fā)現(xiàn),2階差分后序列的波動(dòng)幅度反而變大了(方差更大了),而它的自相關(guān)系數(shù)正負(fù)變化得更為頻繁。雖然序列｛D2p｝也是平穩(wěn)的，但是與｛Dp｝相比，它不是最理想的。4擬合模型，預(yù)測(cè)未來(lái)一年的月度水平(接第2小題)對(duì)異方差的直觀檢驗(yàn)完畢，為構(gòu)造ARCH模型，進(jìn)一步進(jìn)行LM檢驗(yàn):1)使用regress命令對(duì)Dp進(jìn)行MA(1)回歸regressDpL.Dp2)計(jì)算LM統(tǒng)計(jì)量進(jìn)行檢驗(yàn)即：estatarchlm,lags(1234)=>_e；5t.atarchlm,.1234)LIIt.estfdraut.ijregressivecomiit.iurialhetercsksdagticity(ARCH)lags.tp)chiZdfProto>ch.i^12_02110.1545220_04292S.32530_03?fi弓3.0914HO:noARCHeffect^vs.Hl:AUCHCp).disturbEince當(dāng)ARCH模型中的自回歸項(xiàng)數(shù)為(p=)2,3,4時(shí)，LM檢驗(yàn)統(tǒng)計(jì)量的P值小于顯著性水平0.05，拒絕原假設(shè)，認(rèn)為殘差平方序列方差非齊，且可用ARCH模型擬合該序列中的自相關(guān)關(guān)系。(Ps.ma(1)指的是對(duì)｛Dp｝建立ma⑴模型arch(1)指的是對(duì)｛Dp｝的殘差項(xiàng)建立滯后為1期的條件異方差模型)1自回歸項(xiàng)數(shù)為1(p=1)八我的文SVjjrice.dla-[Results]If^prWindhwH^lpS?n：a_ies3tables^,aridt?stsLinearmodelsau.drelatedBlnaryoutcomc>EOrdinaloutcomesCitefforicaloutcomesCountoutcomesTre-itmenie￡￡tatsNunLierofobsEndog^uouscovai'iatesMiltivariatetinesariesL&ngitiid:nal/paiteldataMultilevelmixed-affectsmadelsSurvivalanalysisEpidemiolocyandrelatedSurveyd：itaar^alyEiMiltiple1npatatiduWaldchi￡(1)SetipmdutilitiesARTM4andAMKKmodelsiBCH-'GAKHiKFIIIAmodelsVnob^erved_conporient5nodelPraii_^instenresressionB.eET5E^ionvithBewey-IVeEtstterrorsSta.t:—spacem[>delsrorejasiliLgKRCHor2CAJJJCHmads：lsITelKnsEGKEHn<hi-eshol>1A^RCHmadelGJREorno￡thi-esh&liAJEHn崩el￡iTipLeisymnctrickRCHrriodeLPourerXBJCHncddJorJ-inearA3lCHmawi+Konestii￡tMMd.Model/MMd.3]PrimiD-Elv/i.f/itlModelI1eperLd^ntvari=able:Tr-arLEformation.o￡coad.it3onixl?zii'iariCQforAl[SuppressCOJIEMultivur:ataan.flJ.vEierostistimatioilAECH-iD._mc口】tionsIIzicL'ud.c：AF1CH-lil—tieternini.114m電口TLwqKIndnpindentv：=Lt_La蜀5ofconditiortalysriwest(use5s)Tnbolizet]M：±inme-dt：lEpscifi-zatierL(*)SpHi：ifyri^iiTiuriLags：iEIHAtiadalEpacifica.ti.Gii?AEIHACp,iq]Ejecification:Model2Model3KELCHm公HmunilagGAJLCHmijiTilag0ZAutorearesGiveorder(p)Integrated(difference)order「岳arch-Autoiegressi^ecauditional=>archDp.ai?ch.<1/1)arinia(0Of1JnoLogIIAdisturbELticesARCHIIAdisturbELticesNi.iuirierc>fobs25110-C9Loglikelihood=-1599.541252I,小Qi10-C9Loglikelihood=-1599.541252I,小Qi口膈251DffaldcliiZ(1：>19.27Loglik&liliL-od-1599.71Pr-jb>clii2OPGDp'Coef.Std-Err.zP>IzI[95%ConE.Interval]知_cons6-37063311.453370.560.578-16077572SS1S83AiummaLI..3027854.07004164.320.000.1555064.4400643MICHarchLI..38544.09764293.950.000.1M0636.5768165cons15114.26731.127220.670.00013681.2816547_24arclhDp.iu>const-ant--u?c=h(1/1)0.0r1_]nologWaldchiS^l)Prob>chLZMkdisturbsiicMkdisturbsiic旦sLIPGUp：Coe￡.St-d.Err_sP^-1e|[95%Coil￡_Intervrs_l]KRtSRDiElLI._902954.06901224_390000_1￡T692￡.4382154A￡CHarcl±LI.3B40355.094090C4.080000.1936214_5￡S4497cons15145_(O70T.033121.43000013763_3316534.85ii自回歸項(xiàng)數(shù)為2(p=2)或者archDp,arch(1/2)arima(0,0,1)nolog=>.archDparchfl2)ar±m(xù)a(Or0r1JnoLogARCHtamilyregression--HAdisturbancesSainpLe:z-Z5ZNiunxieror0135=Z51D1strIbutlon.:Gaussian.WallchlZ(1)=±2.12LogLlkelinood=-1534834Prob丁dilZ=o.eoasOPGDpCof_St-d.Err.zP>I=|[95^Conf.Interval]Dp_con=2.17O4C2±2.SC359o.i7o.occ-aa.0421127.：^{l2241LEUEIII□.Li.a.4ftn.fliflii-usaiasAJRCMsrch.LI.-2713154-U9W42S2.800.005-081497，.4^11132LZ..1253-06344181.980.047.0015563.2502437_cons13727.€631415321.740.00012490.0414365.15archDpnoconst--ant-arch(1/2)Ar±m(xù)a(0,0.1)nologARCHfamilyregressiLm■-1IAdisturbannesSample:2-2?i2Ni.ullLierOfCihi：=251Distribution:Gdussl-anWaldchiZ(1)=12_63Loglikelihooc1=-1594.313Prob>chi2=0.0004如?PPGCoef.Std.Err.zP>IzI[95%Conf.Znterval]AIUdAmmLl_.332475-09356683.550.0001450K14.5158626MtCHarctiLl_.2719405一09576132_840.005.0842519.4596292L2_.12C454.0￡J21412000.04￡.0024J91_2504￡fi9GQX1513710.6611.461822.42Q.OOV12512.1614305.05iii自回歸項(xiàng)數(shù)為3(p=3)同理得：

ARCHfaiu-ilyregression—IIAdistu.rtaticesSample:2一252NtullIlierofobs=251Dist-ribu.tion:Ga.usslanWaldchi2(!；■=27.7SLoglikeliliood=-1511.482Prolj孑chiZ=0.0000UpCoe￡.OPGErr.z1z1【gConf.Iixterval]BP_cohe-1_18290&7.993903-0-150.882-ZL6_8506714.48485MUGkmaLI.-3480662.0C604055_270.000_2186292-4775032ARCHarchLI..3109709.102491t3039^002.110091一5118509L-2..10TJ517.063274l.Cl(JT10S)-.022263L3..071777S6.370~W0-3167796-5981434cons6350_162858.0447_400.0004668.4278031.89SL2前的系數(shù)顯著性檢驗(yàn)無(wú)法通過(guò)，建模停止，確定ARCH模型的自回歸項(xiàng)數(shù)為1或2：p=1時(shí),h(t)=3+4…2(Stata語(yǔ)句).archDp,noconstantarch(1/1)a