時(shí)間序列Stata操作 題4-7

1、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）110211511093111811681118108511351138113512351301128312501210113510851060110211511127122612171215125012101268140214861534156715851717200220862059125012101268140214861534156715851717200220862059242523262176212120002000185016401700192

2、518501830185017901700170017501775192520001975194018891881200020241900175016491601162516091649164016401620159015261451142414241329119911791285134912651299137314401451137613251261119912191250127413651424142013851321123512151310131913191279148119562165212520871895184018741863183618942105215921312029227

3、024112652329433603686359334823615396343284309433643824326400940004070420042784435477248124908485748654711464048774902488448334903496348044679481045714250385037753357294623421994242024642763299331082729252524572136227221752100206819551950196920251726157917681766162116921634175016201515150815251502137

4、41212119811071052106910501098115011261200119310581043102698097610001210126411501117118811001040102811131154135017221616152514031497152215501575153816501800193322192606256324331檢驗(yàn)序列的平穩(wěn)性（Stata語(yǔ)句）.dropB-T.generaten=_n.renameAprice.tssetntimevariable:n,1to252delta:1unit.tslineprice=0001price的時(shí)序圖由時(shí)序圖觀測(cè)得p

5、rice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).acpriceeOO1ODOcirpfosnoitalerocotuCOO010203040LagBartlettsformulaforMA(q)95%confidencebandsprice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)?？紤]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)序列的方差齊性先對(duì)原序

6、列做一階差分：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.labelvariabirceleDpfirstdifferenceofirppricefoe.tslineDp=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）od-opacpDfosnoitalerocotu02nVcoo3001020LagBartlettsformulaforMA(q)95%confidencebands40Dp的自相關(guān)圖由圖可見(jiàn)，短期（5期）內(nèi)瓦便衰減直逼零值，衰減速度非?？?，明顯具有短期自相關(guān)性。兀在

7、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:爲(wèi)工0。因此，Dp非白噪聲序列,有信息待提取。預(yù)處理完畢，開(kāi)始識(shí)別模型:od-opDfosnoitalerocotu304001020LagBartlettsformulaforMA(q)95%confidencebandsDp的自相關(guān)圖Stata語(yǔ)句).pacDpOtopDfosnoitalerocotualaitra0X100102030Lag95%Confidencebandsse=1/sqrt(

8、n)40Dp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。ARIMA模型HeperLderitvariatile:coastant132_D丄6UU7184811.：23677或者arimaDp,arima(1,0,1)2(1)Model2Model3by/if/ineightsSIndepeiLiiirLtvsrableE：MAIHIAfp,d,q)specification：0CIntegrated(differPs.同arimaprice,arima(1,1,1)結(jié)果ii認(rèn)為瓦1階截尾，0kk拖尾，嘗試MA參數(shù)顯著性檢驗(yàn)通不過(guò)冒ama-AKXU,AEIAK,and

9、otherdARI1IAregressionModaldd.jKuJ.皀.3by/iE/in.SNijazie2EXDependentv：sriableDpImiependentv：iriablesARIMXmodtlspecificationAUMA(p.(L心specification：aoHoviiLg-averageorier(q)Au*tarazeivaord.arGJZEntegrated(differea匚亡)arder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,

10、1,1)得到結(jié)果白噪聲檢驗(yàn)（Stata語(yǔ)句）.predictehat1,residual.wnteftqehat1PortmanteautestforwhitenoisePortmanteau(Q)statistic=45.3466Probchi2(40)evPs.a0.2589Loglikelihood=-1607.717Dp.Coef.OPGStd_ErrzPIzI95$Conf.IntervalBPcons5.27709512-5410.42（一石-19.31292.UCC99AJU1A1113.LI.337111.04917?76.870-000.2413205.434101/Eiai

11、oa146.35633.53735441-370-0001394233153.290.UUUUWalduhiZ|1JProbcliiZIISupTirezsconst：mtt截距項(xiàng)不顯著AE.IMAregressionSamrile:252NumljerofobsWald口hi仝PtoLi，ch.225147.18llElLl_/Eiiama.wntestqehat1,lags(2).wntestqehat1,lags(6).wntestqehat1,lags(12)都通過(guò)了.wntestbehat1=.estaticOPGCoef-Std.Err.33S0741.0489113146419C

12、3.50909141.730.0C095%Conf.Int-erva丄139J5419433S3E5153.2913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-NoiseTestCO4CD0OODOOtoQNOQoo0.0000.400.50FrequencyBartletts(B)statistic=0.70ProbB=0.7145殘差項(xiàng)是白噪聲序列，計(jì)算AIC/BIC：通過(guò)了白噪聲檢驗(yàn)，但這個(gè)檢驗(yàn)的前提是同方差I(lǐng)口delOhsllCm-illI11(iuoddJdt廠心-251-1607.309

13、23219.fill322.668=ii認(rèn)為瓦拖尾，0kk1階截尾，嘗試AR（1）一AKIUjARIA%andotherARIHAregressionSsoiple:2-252Bependjentvtcriable弧7:BIndepindentvariables.CSuppreseconstanttAEJMAnodfiilEpeificution.(*JaAiTFIA(jIij)specslcatiqxi：Autoregiesslveorder(p)Iniegratmd(differsnce)orderMoving-Avarh.gaordbr(q)Mi.mtierdfobsWaldahi2(1

14、)Proh：匚lii225172.74O.OODODPCoat.OPG営七cl.Err.z21n|Conf.InJtDo_ccns5.10151914.382010.35foT?23-23-036733.28974arJLI.3559392.0411353H-53u.uuu.2141395.3713/sigma145.C5123.41.41D.COOUQ.7554152.507Loyliktliliood1C9C-55J截距項(xiàng)不顯著AB.IHA.regression去掉截距項(xiàng)再試(Stata語(yǔ)句).arimaDp,noconstantarima(1,0,0)Simple:2-252NiiiLL

15、kerofobs=251WaldchiZ(1)=72.=LLLuglikelihood=-1696617ProLchi2=0.0000DpCoef.OPGStd.Err.P|3|95%Conf.lutervalansiarLI.35S875C_04173663.550.000.275D734438C778/Ei3iiia14572123.50517341.570.000138-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.wntestqehat2Portmanteautestfo

16、rwhitenoisePortmanteau(Q)statistic=mPrchi2(40)Ps.040.35160.4547.wntestqehat2,lags(2).wntmstqehat2,lags(6).wntCstqehat2,lags(12)都通過(guò)了.wntestbehat2001QDOOanoOto02nVQooStata語(yǔ)句)differencesn.acS12Dp=.pacS12DpSfosnoitalerocotualaitraod-o0X10coo0X10.od-o.ODO.95%Confidencebandsse=1/sqrt(n)因?yàn)榍笆?一年)內(nèi)可和叮明顯跳出了

17、2倍標(biāo)準(zhǔn)誤范圍，所以確定ma(l),ar(l)，與上面i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。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步差分后序列的自相關(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。.generateD12Dp=S12.Dp.labelvaria1SbleS12Dp12stepsoftheS12Dp的偏自相關(guān)圖加法季節(jié)模型i瓦1階12階截尾際拖尾，結(jié)合疏系數(shù)模型，對(duì)序列S12Dp擬合MA(1,12)模型ii瓦拖尾瓦1階12階(13階)截尾，結(jié)合疏系數(shù)模型，對(duì)

18、序列S12Dp擬合AR(1,12)或AR(1,12,13)模型iii綜合考慮瓦和兀k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IrLdeperLiientvariables：AEZMArTiodslspecific：=ltionModel2Model3bv/if/inWeigtitsSE/RobustReportingMaximizationDependentvai-1abl己：或者(Stata語(yǔ)句).arimaS12Dp,ma(1,12)=AP.IIIAregressionNluilI：ierofobsWaldchiZ(

19、2JLoglikelihood=-1551_408Prob：=chiZSlEDpCoef.OPGStd.Err.zPIzI95%Conf.IntervalS12Dp_cons-.1631442.783658-0.06匕乎啰-5.6190145.292726MJfflmaLI.1366809.06191032.210027.015339.2580225L12.-.9075633-0768C58-11.810-000-1.058217-.7569091/三igma151.32446.334823.890-000138.9084163.7404去掉截距項(xiàng).arimaS12Dp,noconstantm

20、a(1,12)=AP.IMAregressioij.Saiiip1e:14-252MuiLLtierofobs=239Waldchi2(2)=167.45Loglikelihood=-1551_409Probchi2=0.0000S12DpOPGCoe.Std_Err-z|z|954Conf.IntervalAiummaLI.LIZ.13696080618162.220027.0158031258118-.9070947.07C7165-11.820.000-1.0574567567332/migma.151.3393E.32728223.920.000138-53811C3.7406.pre

21、dictehat3,residual.wntestqehat3PortmanteautestforwhitenoisePortmanteau(Q)statistic=62.1168Probchi2(40)=0.0141Q統(tǒng)計(jì)量的P值chi2(40)=0.0037失敗I1ort-iLLiLtiteau.(QJstatis七it:=61.1895.arimaS12Dp,ar(1,12,13)在wntestq時(shí)也失敗了Frot，chlZJ=00111iii對(duì)序列S12Dp擬合ARIMA(1,12)(1,12)模型Portmanteau(Q)Statistic=32.1318.arimaS12Dp,n

22、oconstantar(1,12)ma(1,12)在wntestq時(shí)也失敗了Protlchi(40)=-7858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。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ARMANI

23、)?即MAI?模型提取序列S12Dp的季節(jié)自相關(guān)信息。綜上所述，(對(duì)原序列)擬合模型：ARIMA(1,1,l)x(0,1,1)12ModelModelModel3Ibv/if/inWeishtE2】Ilepindentv：=Lt_1!IrLileperLileiLtt-：=ltiallies!ARIKljARMAXjand.oherMdelModelZby/if/i；nSe-:clii2Loglikeliliood=-154A_217AP.IHAreyressi口nSlEDp口EGStd.ErrS璃1H195%Coni.Int-ervalSIZBp_COI1S-SZ59T322.25918Z-

24、0.410.682-h.35388?3.501942AKObLfLI.3108391.129548C2.0_004_1169292.624150JiiiaL03U3316.1585357-0.IS0.847-.3412619.28019CSAimii2maLI.999哎專0卻275.S477-0.M6.597-541.515539.515/siiipiLa141_020519448.810.010.49703825?.mm截距項(xiàng),參數(shù)和參數(shù)012均不顯著。0-ADOA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?；氐紸RIMA模型:由于對(duì)Dp構(gòu)建的MA（1）模型（無(wú)截距項(xiàng)）較好，觀

25、察該模型的殘差圖和殘差平方圖（Stata語(yǔ)句）.tslineehat1呂G0口口1?OSTdtDJSi.u口-emga50100150200250nARIMA(O,1，l)(noconstant)的殘差圖1從殘差圖看，方差變化幅度較大，參差不齊。.twoway(connectedehat1nin1/252)=050100150200250ri呂s0口弓口呂L-enEgaARIMA(0，1，1)(noconstant)的殘差圖2.generatee12=ehat1*ehat1(1missingvaluegenerated).twoway(connectede12n)50100150200250r

26、i口呂口啟匸呂口尋呂口呂0ARIMA(O,1,l)(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(jiàn)，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)

27、間序列波動(dòng)不大。自相關(guān)圖在第2小題里：od-o0X10QOOod-o.甲14*010203040LagBartlettsformulaforMA(q)95%confidencebands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)圖十1lyl由時(shí)序圖

28、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):使用regress命令對(duì)Dp進(jìn)行MA(1)回歸regressDpL.Dp計(jì)算LM統(tǒng)計(jì)量進(jìn)行檢驗(yàn)即：estatarchIm,lags(1234)=_eistatarchlm,.1曰1234)LIIt.estfdraut.ijregressivecomiit.iurialhetercsksdagticity(ARCH)lags.tp)chi

29、ZdfProtodhig12_02110.1545220_04292S.32530_03fi孕3.0914HLi：noARCHeffedssvs-Hl:AP.CHrp)dist-urbailee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ma模型arch(l)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)i自回歸項(xiàng)數(shù)為1(p=1)ProbcIliZEGKECHnop-ILrrmd-a.lIostdstupatjOILLag

30、sofconditictlsIyariajicatIInjaLudc：AF1CH-ln.-ti4ternitli.114ABZM-iD.me工口djitioilsSwm：dfies3tableandtstsLinearmodelsau.drelatml卜*IBlnaryoutcomcEOrdinaloutcomesiCtefforicaloutcoineriCi)untoutcomestC4XVWaJ.1Z41X3.X*ajrTiCi-=1EKdTre-itmenietats卜DEndogenouscovaiia.its卜uSample-stiestionncdelskE:cactstlst.

31、1askIT卽珂arun4triaiskJTimeseriesMiltivariatetinesariesLungitiid:nal/paneldataMiiltllevelmixed._EffectmodelsSurvivalanalysis-J-Epidemiolocyandrelat顯n.SEM(strueale11-3.t.iextmodlirgJ卜SurveyditaarsalysisMiltlpleimpiitationMultivur:ataan.flJ.vEiekI1ependH：rLtv：=ltible:IrLdHpnderd戸：丑SetiDmdutilAMIVkandAMK

32、XmodelsABCH-fGAKHAKFIBAmodelsUnob弓Etrved-conDDriEiit呂nodelErin呂tinB.eErEionvithBewey-IYeEtstlNode/ModallPrLminEIv/lf/in=archDp.ai?ch.chiZOPGCcef.St-d.Err.95%ConE-IntervalBpcons6-37063311.453370.578-1607757281S83AiumLl-.3027854.07004164.320.000.1555064.4400643MtCHarchLl-cons-38544.0976429731-12720.00

33、00.00013681.28.576816516547.24Mkdi蘭turbsiic色sARCHfsiikilyrtgrtissiuii252251Dist-ribi.iti口血:GwssiaoiDffaldcliiZ(1：19.27Loglik&liliL-od-1599.71Pr-jbclii2Up：LIPG2|h|95%Conf.IntsivtslICoe.囂七cLErr.KRtSAIllSlLI._902954.06901224_J9ooao_1T692_4382154ACHarclLI.3B40355.094090C4_08ooao.1936214_5S4497cons15145_

34、(O707.033121-43ooao13763_3316534.85ii自回歸項(xiàng)數(shù)為2(p=2)Moh1jRodeL2|卅口日乞.3|Farining|：by/if/in|riilu|SE/Robost.|REiiuri.i:n.F|Rtuciiijcalian|Suppressconstantterninfillmodelsp4cifscqlLLon.1:AECHnLFiUFi屯121-CJJE.CHnLEiunLn蕓*：*)Supply11stolags：(eARCH1=GARCHlacLOPe，=iyffiacinwilgs：Model2中設(shè)置不變或者archDp,arch(1/2)a

35、rima(0,0,1)nolog=.archDprarchfl2)arma(OQ.1JnoLogARCHtaniilyregression-I1AdisturbancesOPGmum2-17O4C212.0.17O-OCC-29-0421127.30224LI34BCMsrch.12490.0414?65.15D1strIbut1on.:Gaussian.LogLlkellliood=-15M834nani-1.453795.0814?7.4(11132-0015563：.2502437cons13727.66B1415321.740-000NiuniierorodeZ51WallchlZ(1

36、)12.12Prob袞dilZ0.000595ConfInterval.2713154.D9C84252.800.005.1259.D6344181.980.047zMUIAHlElarchDp,.noconst-ant-arch(1/2)Arma(0,0.1)nologARCHfamilyregressiLm-HAdisturbannes丄2.30-0004LIMtCHarcti611QG；L&12512161430S.Q5Coef.Std.Err95%Conf.Interval.332475.0935668.1450S14.0957613.0842519.4596292.0J2741.00

37、24J91.2504CS9GQX1513710G000QNi.ullLierofcbs：WaldchiZ(1)Loglikelihood=-1594.313Probchi2LI.27194052_840.005L2.1264542.000.04iii自回歸項(xiàng)數(shù)為3(p=3)同理得：ARCHfaiu-ilyregressionIIAdisfurtaticesSample:2-252NtullIlierofobs=251Dxst-ribu.tion:Ga.usslanWaldchi2(l；i=27.7SLoglikeliliood=-1511.482ProLachiZ=0.0000Coe.OPGS

38、i-d.Err.z1z1【9占?xì)癈onf.IixtervalBP_cohe-1_18290&7.993903-0_150.882-ZL6_8506714.48485MUGkmaLI.-3480662.0C604055_270.000_2186292-4775032ARCHarchLI.3109709.102491t303.110091-5118509L-2.10TJ517.063274l.ClQo.iosj)-.022263.2257CC5L3.071777S6.3705981434cons6350_162858.0447_400.0004668.4278031.89

39、SL2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+(Stata語(yǔ)句).archDp,noconstantarch(1/1)arima(0,0,1)nolog.predictehat,residual(1missingvaluegenerated).wntestqehatPortmanteautestforwhitenoise45.13660.2659Portmanteau(Q)statisticProbchi2(40).wntestbehat001CD0Oaoood-oCNOQOOP值均大于a,殘差列通過(guò)白噪聲檢驗(yàn)。.estaticModel|-L+Obsll(null)ll(model)dfAIC.|251.-1599.7133205.42AkaikesinformationcriterionandBayesianinformationcriterion之前的