时间序列Stata操作 题4

1102115110931118116811181085113511381135123513011283125012101135108510601102115111271226121712151250121012681402148615341567158517172002208620591250121012681402148615341567158517172002208620592425232621762121200020001850164017001925185018301850179017001700175017751925200019751940188918812000202419001750164916011625160916491640164016201590152614511424142413291199117912851349126512991373144014511376132512611199121912501274136514241420138513211235121513101319131912791481195621652125208718951840187418631836189421052159213120292270241126523294336036863593348236153963432843094336438243264009400040704200427844354772481249084857486547114640487749024884483349034963480446794810457142503850377533572946234219942420246427632993310827292525245721362272217521002068195519501969202517261579176817661621169216341750162015151508152515021374121211981107105210691050109811501126120011931058104310269809761000121012641150111711881100104010281113115413501722161615251403149715221550157515381650180019332219260625632433《应用时间序列分析（第四版）》王燕编著中国人民大学出版社第四章习题71974年1月至1994年12月，某地胡椒价格数据如下：（21行*12列）1检验序列的平稳性（Stata语句）.dropB-T.generaten=_n.renameAprice.tssetntimevariable:n,1to252delta:1unit.tslineprice=>{price}的时序图由时序图观测得price变化落差很大，该序列不平稳。再看看自相关图：・・・(Stata语句).acprice-CRrprosnoLLaleFDCD.UA010203040LagBartlett'sformulaforMA(q)95%confidencebands{price}的自相关图短期（延迟阶数为5期及5期以内）来看，自相关系数拖尾；长期来看，自相关系数缓慢地由正转负，一直是下降趋势。序列值之间长期相关，该序列非平稳序列。（Ps.平稳时间序列具有短期自相关性。）结合之前的时序图，发现该序列具有明显的长期趋势。考虑到price是月度数据，因此觉得该序列很有可能还•••••••••••存在季节效应。2检验序列的方差齐性原序列具有长期趋势，所以需要平稳化。（Stata语句）.generateDp=D1.price.labelvariableDppprice"oe.tslineDpe=>firstdifferenceof先对原序列做一阶差分:QUO1-｛Dp｝的时序图（一阶）差分后序列｛Dp｝的长期趋势不再明显，平稳化效果很好。再看看｛Dp｝的自相关图:（Stata语句）qdfosno.^ae^pcoruA010203040LagBartlett'sformulaforMA(q)95%confidencebands｛Dp｝的自相关图由图可见，短期（5期）内标便衰减直逼零值，衰减速度非常快，明显具有短期自相关性。％在延迟1期以后，除了当k=30时跳出过阴影范围，其余全都落在2倍标准误的范围内，围绕着零值做很小幅（约土0.1）的波动。因此，｛Dp｝是平稳的时间序列。平稳性检验通过，看白噪声检验。自相关图明显显示：宙力0，咬力0。因此，｛Dp｝非白噪声序列，有信息待提取。预处理完毕，开始识别模型:QDfosno.LalerrocoTUA2-0111010203040LagQDfosno.LalerrocoTUA2-0111010203040Lagn_Dfosno.ta.eKrocoTuala.Trap1020Lag95%Confidencebands[se=1/sqrt(n)]3040{Dp}的偏自相关图(1)不考虑季节效应，先试ARIMA模型，再试疏系数模型。①ARIMA模型i认为祢和虹都拖尾，尝试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)结果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参数显著性检验通不过ii认为祢1阶截尾，0kk拖尾，尝试蛔(1)酮ari>a-AKI1A.AEIAK,andotherdModal.Md,■|JoJ己].3||壬Dependentvariable：Imiependentv：ii_iables：IISupTirassconst：mttAJLlMXmodtlEpecificitio^.,J*■AHWA(p,土电)specification：Au*tarazeivaord.arZEniegrated(differenceJarierHoving"averageorier(q)去掉截距项再试(Stata语句)arimaDp,noconstantarima(0,0,1)Ps.结果同arimaprice,noconstantarima(0,1,1)得到结果白噪声检验(Stata语句).predictehat1,residual.wnteftqehat1PortmanteautestforwhitenoisePortmanteau(Q)statistic=45.3466Prob&chi2(40)=0.2589evPs.m.wntestqehat1,lags(2).wntestqehat1,lags(6).wntestqehat1,lags(12)都通过了.wntestbehat1=>.estaticARHIAregression£.~iTiip：2-252HumJou£afohsWaldchiZ|1J-251■47.15Loglikelihood=-1607.717Prob>cluZ=u.uuuuDp.Coef.OPGStd_Err»zP>IzI[泪Conf.Interval]BP_cons5.27709512-0.42-19.31292^.UCC99AJU1A1113.LI..337111_04917?76.870-000.2413205.434101^/Eii3ioa146.35633.53735441-370-0001394233153.29截距项不显著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对｛Dp｝构建MA（1）模型（无截距项）成功，对残差项进行白噪声检验CumulativePeriodogramWhite-NoiseTestCO4aoodooOtoCNOQoo0.0000.400.50FrequencyBartlett's(B)statistic=0.70Prob>B=0.7145通过了白噪声检验，但这个检验的前提是同方差残差项是白噪声序列，计算AIC/BIC：llodclOhsllCm-illI11(luC-dclJdtAICETC"-251-1607.3092'\3219.fill322«.66S=>ii认为祢拖尾，0kk1阶截尾，尝试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去掉截距项再试截距项不显著AEIHA.regression(Stata语句)Simple:2-252NiiiLLkerofobs=251WaldchiZ(1)=73.11Laglikelihood=-1696617ProL>chi2=0.0000.arimaDp,noconstantarima(1,0,0)(Stata语句)DpCoef.OPGStd.Err.zP>|3|[95%Conf.luterval]皿SIarLI..35(875(_04173663.550.000.275D734438C778/Ei»3iiia14572123.50517341.570.000138-B512152.5912对｛Dp｝构建AR(1)模型(无截距项)成功，对残差项进行白噪声检验白噪声检验(Stata语句).predictehat2,residual.wntestqehat2PortmanteautestforwhitenoiseePortmanteau(Q)statistic=m>chi2(40)=40.3516CumulativePeriodogramWhite-NoiseTestPr0.4547Ps.0.wntestqehat2,lags(2).wntestqehat2,lags(6).wntCstqehat2,lags(12)都通过了.wntestb.wntestqehat2PortmanteautestforwhitenoiseePortmanteau(Q)statistic=m>chi2(40)=40.3516CumulativePeriodogramWhite-NoiseTestPr0.4547Ps.0.wntestqehat2,lags(2).wntestqehat2,lags(6).wntCstqehat2,lags(12)都通过了.wntestbehat2QU1QDOOanoOtoaMOcoo0.0000.400.50FrequencyBartlett's(B)statistic=0.67Prob>B=0.7551因为前十二期(一年)内宙和011明显跳出了2倍标准误范围，所以确定ma(1),ar(1)，与上面①i对｛Dp｝拟合ARMA(1,1)的情况一致，已经知道拟合不成了。(2)换季节模型，先试简单的加法模型，再试复杂的乘积模型。步差分后序列的自因为考虑了季节因子，这里是月度数据，所以要对一阶差分后序列进行12步差分。观察12相关系数和偏自相关系数的性质，尝试拟合季节模型。=>.pacS12Dpfosnorta.eFDCO^Uala.Trap.generateg12Dp=S12.Dp.labelvariableS12Dp"12stepsofthedifference'步差分后序列的自尝试拟合季节模型。=>.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}的偏自相关图①加法季节模型i祢1阶12阶截尾%拖尾，结合疏系数模型，对序列｛S12Dp｝拟合MA(1,12)模型iiR拖尾虹1阶12阶(13阶)截尾，结合疏系数模型，对序列｛S12Dp｝拟合AR(1,12)或AR(1,12,13)模型iii综合考虑R和虹几阶截尾的性质(哪几期延迟期数对应的相关系数特别明显)，对序列｛S12Dp｝拟合ARIMA((1,12)(1,12))模型AEZMArncidilspecificationModwlAEZMArncidilspecificationModwl2Model3bv/if/inWeigtitsSE/RobustReportingMaximization.Dependentvai-1abls:IrLdeperLiientvariables：或者(Stata语句).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去掉截距项.arimaS12Dp,noconstantma(1,12)=>.predictehat3,residual.wntestqehat3PortmanteautestforwhitenoisePortmanteau(Q)statistic=62.1168Prob>chi2(40)=0.0141Q统计量的？值<a,拒绝原假设，认为残差列非纯随机，序列｛S12Dp｝中还有信息未提取完毕，建模失败Iii对序列｛S12Dp｝拟合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失败I1ort-iLLiLtiteau.(QJstatistic=61-1895.arimaS12Dp,ar(1,12,13)在wntestq时也失败了PEOb*J=00111iii对序列｛S12Dp｝拟合ARIMA((1,12)(1,12))模型Portmanteau(Q)■Statistic=32.1318.arimaS12Dp,noconstantar(1,12)ma(1,12)在wntestq时也失败了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｝所具有的短期相关性和季节效应用加法模型无法充分、有效提取，这两者之间具有更复杂的关系，不妨假定为乘积关系，尝试用乘积模型来拟合序列的发展。②乘法季节模型先考虑｛S12Dp｝的短期相关性。观察12阶以内（包括12阶）的自相关系数和偏自相关系数，两者均拖尾，所以尝试用ARMA（1，1）模型提取差分后序列的短期自相关信息。再考虑｛S12Dp｝的季节相关性（季节效应本身还具有相关性）。观察以12期为单位的自相关系数和偏自相关系数，前•・・・・・.者1阶截尾，后者拖尾，所以用以12步为周期的ARMA（0,1）12即MA（1）12模型提取序列｛S12Dp^季节自相关信息。综上所述，（对原序列）拟合模型：ARIMA（l,1,l）X（0,1,1扇归—ARIULjA"RTAXjath&rd：Mod乩|血匝LW||血匝L3|[b”iHin]|脸曰心||浏Hepindentv：=Lt_i=±ti]_e:IndepemleTLiialiies:S12B?vjS-OSuppress应玷tanttcAJtZNAmodelspecificaticn1nA-utoregi-essiwecrierLpJ0Intepi：-=±tedlsdi£±erencejorder1*Movln厂averagedriertq)

-.ARIVAjARMASf理do^herM<delModelZModel.3bv/if/inheights5mms-:<rL：=ilAILLHAspeciticitiqil®SATiIMACF..D,Q,S)specification0tAutpr如-[F；iQ*Iiityg3-ated(.ilifterenne)order1Mcivin厂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.顿fl.997-541.£515539.^515/siiipiLa141_020519448.810.010.4970：J825?_9?截距项，参数有和参数％2均不显著。季节效应如此明显的序列｛S12Dp｝居然难以构建乘积季节模型。回到ARIMA模型:

由于对｛Dp｝构建的MA（1）模型（无截距项）较好，观察该模型的残差图和残差平方图（Stata语句）.tslineehat1=>□50100150200250nARIMA(0,1,1)(noconstant)的残差图1从残差图看，方差变化幅度较大，参差不齐。.twoway(connectedehatlnin1/252)=>050100150200250nARIMA(0，1，1)(noconstant)的残差图2.generatee12=ehat1*ehat1(1missingvaluegenerated)

.twoway(connectede12n)□50100150200250nARIMA(0,1,1)(noconstant)的残差平方图Ps.tslinee12也可以得到残差平方图(同均值的残差序列的方差就是残差平方的期望，)残差平方图上的异方差性太过明显了。3考察序列的差分平稳属性，并考察过差分特征差分的目的是平稳序列。过差分，过多次数的提取信息，虽然提取掉了非平稳的确定性信息，却浪费了更多的其他信息。第2小题中，我对原序列进行了1阶12步差分，从时序图和自相关图可见，1阶差分后序列｛Dp｝变平稳了，如果再考虑季节因素，对｛Dp｝进行12步差分，得到序列｛S12Dp｝，它的时序图为：时序图显示，虽然序列｛S12Dp｝具有集群效应，但从整个观察期来看，多数时间序列波动不大。自相关图在第2小题里：

Oto-0102030Lag400—Bartlett'sformulaforMA(q)95%Oto-0102030Lag400—自相关图显示，短期内延迟一阶后序列｛S12Dp｝的自相关系数即落入阴影区域内，之后，绝大部分滞后期的自相关系数也在阴影范围内。序列｛S12Dp｝短期自相关，比较平稳。过差分的情况会是怎样？在Stata中尝试对序列｛Dp｝再做一次差分：（Stata语句）.generateD2p=D.Dp.tslineD2p.acD2p比照2阶差分后序列比照2阶差分后序列｛D2p｝与1阶后序列｛Dp｝的时序图、自相关图：｛Dp｝的自相关图｛D2p｝的自相关图｛Dp｝的自相关图｛D2p｝的自相关图1AIf1oo••4TJtL■11III由时序图发现,2阶差分后序列的波动幅度反而变大了(方差更大了),而它的自相关系数正负变化得更为频繁。虽然序列｛D2p｝也是平稳的，但是与｛Dp｝相比，它不是最理想的。4拟合模型，预测未来一年的月度水平(接第2小题)对异方差的直观检验完毕，为构造ARCH模型，进一步进行LM检验:1)使用regress命令对Dp进行MA(1)回归regressDpL.Dp2)计算LM统计量进行检验即：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当ARCH模型中的自回归项数为(p=)2,3,4时，LM检验统计量的P值小于显著性水平0.05，拒绝原假设，认为残差平方序列方差非齐，且可用ARCH模型拟合该序列中的自相关关系。(Ps.ma(1)指的是对｛Dp｝建立ma⑴模型arch(1)指的是对｛Dp｝的残差项建立滞后为1期的条件异方差模型)1自回归项数为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电口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自回归项数为2(p=2)或者archDp,arch(1/2)arima(0,0,1)nolog=>.archDparchfl2)ar±ma(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±ma(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自回归项数为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前的系数显著性检验无法通过，建模停止，确定ARCH模型的自回归项数为1或2：p=1时,h(t)=3+4…2(Stata语句).archDp,noconstantarch(1/1)a