时间序列Stata操作 题4-7

1、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）110211511093111811681118108511351138113512351301128312501210113510851060110211511127122612171215125012101268140214861534156715851717200220862059125012101268140214861534156715851717200220862059242523262176212120002000185016401700192

2、518501830185017901700170017501775192520001975194018891881200020241900175016491601162516091649164016401620159015261451142414241329119911791285134912651299137314401451137613251261119912191250127413651424142013851321123512151310131913191279148119562165212520871895184018741863183618942105215921312029227

3、024112652329433603686359334823615396343284309433643824326400940004070420042784435477248124908485748654711464048774902488448334903496348044679481045714250385037753357294623421994242024642763299331082729252524572136227221752100206819551950196920251726157917681766162116921634175016201515150815251502137

4、41212119811071052106910501098115011261200119310581043102698097610001210126411501117118811001040102811131154135017221616152514031497152215501575153816501800193322192606256324331检验序列的平稳性（Stata语句）.dropB-T.generaten=_n.renameAprice.tssetntimevariable:n,1to252delta:1unit.tslineprice=0001price的时序图由时序图观测得p

5、rice变化落差很大，该序列不平稳。再看看自相关图：(Stata语句).acpriceeOO1ODOcirpfosnoitalerocotuCOO010203040LagBartlettsformulaforMA(q)95%confidencebandsprice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先对原序

6、列做一阶差分：原序列具有长期趋势，所以需要平稳化。Stata语句）.generateDp=D1.price.labelvariabirceleDpfirstdifferenceofirppricefoe.tslineDp=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）od-opacpDfosnoitalerocotu02nVcoo3001020LagBartlettsformulaforMA(q)95%confidencebands40Dp的自相关图由图可见，短期（5期）内瓦便衰减直逼零值，衰减速度非常快，明显具有短期自相关性。兀在

7、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:爲工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:od-opDfosnoitalerocotu304001020LagBartlettsformulaforMA(q)95%confidencebandsDp的自相关图Stata语句).pacDpOtopDfosnoitalerocotualaitra0X100102030Lag95%Confidencebandsse=1/sqrt(

8、n)40Dp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。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)结果ii认为瓦1阶截尾，0kk拖尾，尝试MA参数显著性检验通不过冒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去掉截距项再试（Stata语句）arimaDp,noconstantarima(0,0,1)Ps.结果同arimaprice,noconstantarima(0,

10、1,1)得到结果白噪声检验（Stata语句）.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截距项不显著AE.IMAregressionSamrile:252NumljerofobsWald口hi仝PtoLi，ch.225147.18llElLl_/Eiiama.wntestqehat1,lags(2).wntestqehat1,lags(6).wntestqehat1,lags(12)都通过了.wntestbehat1=.estaticOPGCoef-Std.Err.33S0741.0489113146419C

12、3.50909141.730.0C095%Conf.Int-erva丄139J5419433S3E5153.2913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-NoiseTestCO4CD0OODOOtoQNOQoo0.0000.400.50FrequencyBartletts(B)statistic=0.70ProbB=0.7145残差项是白噪声序列，计算AIC/BIC：通过了白噪声检验，但这个检验的前提是同方差I口delOhsllCm-illI11(iuoddJdt厂心-251-1607.309

13、23219.fill322.668=ii认为瓦拖尾，0kk1阶截尾，尝试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截距项不显著AB.IHA.regression去掉截距项再试(Stata语句).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.wntestqehat2Portmanteautestfo

16、rwhitenoisePortmanteau(Q)statistic=mPrchi2(40)Ps.040.35160.4547.wntestqehat2,lags(2).wntmstqehat2,lags(6).wntCstqehat2,lags(12)都通过了.wntestbehat2001QDOOanoOto02nVQooStata语句)differencesn.acS12Dp=.pacS12DpSfosnoitalerocotualaitraod-o0X10coo0X10.od-o.ODO.95%Confidencebandsse=1/sqrt(n)因为前十二期(一年)内可和叮明显跳出了

17、2倍标准误范围，所以确定ma(l),ar(l)，与上面i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。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步差分后序列的自相关系数和偏自相关系数的性质，尝试拟合季节模型。.generateD12Dp=S12.Dp.labelvaria1SbleS12Dp12stepsoftheS12Dp的偏自相关图加法季节模型i瓦1阶12阶截尾际拖尾，结合疏系数模型，对序列S12Dp拟合MA(1,12)模型ii瓦拖尾瓦1阶12阶(13阶)截尾，结合疏系数模型，对

18、序列S12Dp拟合AR(1,12)或AR(1,12,13)模型iii综合考虑瓦和兀k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IrLdeperLiientvariables：AEZMArTiodslspecific：=ltionModel2Model3bv/if/inWeigtitsSE/RobustReportingMaximizationDependentvai-1abl己：或者(Stata语句).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去掉截距项.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统计量的P值chi2(40)=0.0037失败I1ort-iLLiLtiteau.(QJstatis七it:=61.1895.arimaS12Dp,ar(1,12,13)在wntestq时也失败了Frot，chlZJ=00111iii对序列S12Dp拟合ARIMA(1,12)(1,12)模型Portmanteau(Q)Statistic=32.1318.arimaS12Dp,n

22、oconstantar(1,12)ma(1,12)在wntestq时也失败了Protlchi(40)=-7858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。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ARMANI

23、)?即MAI?模型提取序列S12Dp的季节自相关信息。综上所述，(对原序列)拟合模型：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哎专0却275.S477-0.M6.597-541.515539.515/siiipiLa141_020519448.810.010.49703825?.mm截距项,参数和参数012均不显著。0-ADOA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

25、察该模型的残差图和残差平方图（Stata语句）.tslineehat1吕G0口口1?OSTdtDJSi.u口-emga50100150200250nARIMA(O,1，l)(noconstant)的残差图1从残差图看，方差变化幅度较大，参差不齐。.twoway(connectedehat1nin1/252)=050100150200250ri吕s0口弓口吕L-enEgaARIMA(0，1，1)(noconstant)的残差图2.generatee12=ehat1*ehat1(1missingvaluegenerated).twoway(connectede12n)50100150200250r

26、i口吕口启匸吕口寻吕口吕0ARIMA(O,1,l)(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

27、间序列波动不大。自相关图在第2小题里：od-o0X10QOOod-o.甲14*010203040LagBartlettsformulaforMA(q)95%confidencebands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的自相关图十1lyl由时序图

28、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:使用regress命令对Dp进行MA(1)回归regressDpL.Dp计算LM统计量进行检验即：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ma模型arch(l)指的是对Dp的残差项建立滞后为1期的条件异方差模型)i自回归项数为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显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兰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自回归项数为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芸*：*)Supply11stolags：(eARCH1=GARCHlacLOPe，=iyffiacinwilgs：Model2中设置不变或者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自回归项数为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占毎Conf.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+(Stata语句).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,残差列通过白噪声检验。.estaticModel|-L+Obsll(null)ll(model)dfAIC.|251.-1599.7133205.42AkaikesinformationcriterionandBayesianinformationcriterion之前的