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1、Contents:StudySession3:QuantitativeMethodsReading6:FintechInvestmentManagement()Reading7:CorrelationandRegression()Reading8:MultipleRegressionandIssuesinRegressionAnalysis()Reading9:Time-SeriesAnalysis()Reading10:ExcerptfromProbabilisticApproaches:ScenarioAnalysis,DecisionTrees,andSimulations()u-EeI
2、zoraraOM-06tj3duol-一ss-g-号V:-euvipitedSPOIIl-H-eu0N4-mteduo55Hc-d-PUe-dlu一SNt3dS-SA-BUXZcora-racra2Q:mUo-SsasAPnlS:匕UBwoUSeSUSVefiS-SsCorreIationAnaIysisCorrelationanalysisScatterplotsSamplecovarianceandcorrelationcoefficientCov(X,Y)Xi-XYi-YCov(XJ)=Fn-lHypothesistestingofcorrelation1.imitationstocor
3、relationanalysisOutlierSpuriouscorrelationNonlinearrelationshipsCorrelationAnalysisHypothesistestingofcorrelationTestthecorrelationcoefficientbetweentwovariablesisequaltozero.Hp=0,H:aPH.t-test:t=ri二2df=n-2.Two-tailedtest.RejectHf:t+tcritical,。t-tcriticalp-value-SlvZSOMOIUOuUo一一0。BS0usUo4JBs-rol-roE-
4、urooororoqoSPUq-EOJoAPnthencewerejectH0.IUp三oUOSS8匿BOJIS2ucrao三Slupso3Uo-SSBg3JoUO4el-e-lu-SUo-IBnbpuroS-PoEUo-SSjJClJOmUo-SS(Sio)S3nbsISB-AJeU-PJOSUo4dlunssPSBrlbSOUJnS:LIJ(IJJSOBPsenbsjoEnS一ON-EZ-E0一Bdo-SPUBIdEllJoJoou三O-SStwJSlouss-(Slo)Salenbslsea-A-Bu-P-Osos三a三lv三三s三IraRegressionmodelsandequati
5、onsForsimplelinearregression:Yj=b0+b1Xi+jV=b+bYFormultiplelinearregression:Y=b+bXj+bX)+.+bkXki+JIUI11Cqlr=b0b1X1i+b2X2+bkXkiSimpleandMultipleLinearRegressionInterpretationofregressioncoefficients/VSlopecoefficient(b)j:sensitivityofYtoachangeinX.Forsimpleregression:changeofYfor1-unitchangeofX.Formult
6、ipleregression:changeofYfor1-unitchangeof%,holdingtheotherindependentvariablesconstant.Interceptcoefficient(b*Forsimpleregression:valueofYwhenXiszero.Formultipleregression:valueofYwhentheindependentvariablesareallzero.SimpleandMultipleLinearRegressionSignificancetestforaregressioncoefficientHb0；H:a*
7、0bTeststatistic:t=1df=-k-l.s-RejectHf:bt+tcritical/Ort-tcriticalp-valueNBO-lH一员jx-一一q上(gsX。一)qjqv(sxJ),.-qjo(SXJ)lqVtrs三LK99ZUSt7。/(0ZU)HlS-1S4-SISSqlZE2“=之-P*IU-七u0uBdo-SajLl-OU一Liulp0一2roUJJo七dCQCMSUV1.33=3三dU一一S+:口sllZHw-roozpPJ3purolsHUJLUS)“0F-criticalvalue.TheF-testhereisalwaysaone-tailedtest.
8、RejectionofHt511eansthereisatleastoneregressioncoefficientissignificantlydifferentfromzero.Atleastoneindependentvariablemakesasignificantcontributiontotheexplanationofdependentvariable.Forsimplelinearregression,theF-testduplicatethet-testforthesignificanceoftheslopcoefficient.H:ObKO,H:bq0.(冰要皿(SS-H整
9、)UOUPBdSSfOJ-qBzEAIUBPUjdBPA-IE-3nQ-qe一eUlapuadapu-EW-enor(史舞#/)AWsw=Ou一n,冰要IEb-0ro-l-l-005S-SA-BUBUOSSJMaJ.三Sanss-S-SA-BlIUIiCHSSaIES-S3nss_Heteroskedasticity:definitionVarianceoftheerrorsdiffersacrossobservations.UnconditionalHeteroskedasticity:theerrorvarianceisnotcorrelatedwiththeindependentvari
10、ables.Createsnomajorproblemsforstatisticalinference.ConditionalKeteroskedasticity:theerrorvarianceiscorrelatedwiththevaluesoftheindependentvariables.Doescreatesignificantproblemsforstatisticalinference.Heteroskedasticity:effectsThecoefficientestimates(b)jarentaffected.Thestandarderrorsofcoefficient(
11、Sqareusuallyunreliable.Withfinancialdata,thestandarderrorsaremostb-blikelyunderestimate,andthet-statistics(t-)Sawillbeinflated,suggestingsignificancewhenthereisnone(typeIerror).TheF-testisalsounreliable.poluUo一SSbolp=nqOIS3nbsIS3-pz=JUOJOs-SJOJJPJBPUCnqOJM.三tioolo4seplso-lHAlpAsepBXSO-BlBlI0H4S9ZXor
12、an-ws-ranp一SJ-oSiO-dl-rotwUASalXlP=SePeXSO-BleHS-SA-EIIVU*三SS3三3H三SalISS-WEOJUBJMlJqu04iz03.arocjj0U-IJo-Iroi=03-roS2El-0e5-cora-too-sodIUORe-BXIOY-roS仁.-sod.Suo-SsSs山E4U-MadAlPUeU一ouraUoI-Ms-l-oo3SILU一0IIlUoA-fcsp-UORe-BXIOJ-B=BSS-SA-EIIV!.三ss0s三SalISS-qe-JUnOS-BS-sl-l-Hdo。-BdAl)IUes三upsou-zro-l-ra
13、rolPnpUoO-1。0。U-poUJ4sJPUnS-1S4B1SJPUBPele-JU-SJOJJepropuels-UOQB-B-UOo-3ss(0-BdAl)UoU-一UCMootMwEelJU一s-sspu3Ee-uSOBro_uro三o-l-l-ou-Js0qe=UnA=BnSnBIU-JO3Os0ZePUBlSBlllpo:P=rasSelBIJU-ISBlu:BoS3111SIo4=:uo-rooo。-e-,lsS-SA-BIIUU*三SS3三3H三Sallss-Serialcorrelation:testingScatterplotsoftheresiduals.TheDur
14、bin-Watson(DW)test.HNoserialcorrelationDecisionrule:In-FailtoIn-PositiveconclusiverejectH0conclusiveNegativeDW=OdLd4-d4-clDW=4(r=l)(r=-l).JS1-Uo4Bnbot-l-BiiiAJ-POIAIs0PJ5puelsIUBP-JJBo0一lsnfpPIlPnpUoO-:P0。U-、p：IeEASPUnSalSAelSJPllBpelSJO-uPjlePUSSqe=8unPUBsp-UJ一-UJJEOOO-SlU-JJOjUo-SSCIjOJJoSEc=ou三3-
15、P3eOj-三Bs-qBeIUBPUBdBPU-UO三UF3Pc=-0u三3IS-SA-EIIVU*三SS3三3H三SalISS-s-qelupudpu-pl-uolJOEOE00M-OM.三c0。：AweU=-O-HnlAloura三UaS-BJorau-VM-PUBIl-llS-ZH-WM、(一SIJ)IUeJ三u-s-SIU-JOJUo-SS七OUoNMun:-一Jlee=84sS-SA-EIIVU*三SS3三3H三SalISS-SummaryofassumptionviolationsViolationEffectsTestingConditionalHeteroskedasticit
16、y与TypeIerrorBreusch-Pagen2-testH0:noHeteroskedasticityPositiveserialcorrelationsj，TypeIerrorDurbin-WatsontestH0:noserialcorrelation0DWcIl:positivecorrelationNegativeserialcorrelations/TypeIlerrorMulticollinearitys/TypeIlerrorNonet-testssignificant,F-testsignificantandhighR2S-qraVBAEUJnPTlJPUMosoOEra
17、-t-3OllUBMM、/L0JO-EUoSBaElPUE-qraera-JoBd-Uo-qBeAEUJna-qe-JleUIaPUadaPU-ra-ra3oS-SA-EIIVU*三SS3三3H三SalISS-Qualitativeindependentvariable(Cont.)Example:Ybb,#b,2f-b妙Eiwhere:Yj=quarterlyvalueofEPSofastock.YXiX2X3QIEPS100Q2EPS010Q3EPS001Q4EPS(omittedcategory)000Qualitativeindependentvariable(Cont.)Interp
18、retationofcoefficient:Interceptcoefficient:theaveragevalueofdependentvariablefortheomittedcategory.Regressioncoefficient:thedifferenceindependentvariable(onaverage)betweenthecategoryrepresentedbythedummyvariableandtheomittedcategory.Practice1WhichofthefollowingisleastaccurateregardingtheDurbin-Watso
19、n(DW)teststatistic?A)Iftheresidualshavenegativeserialcorrelation,theDWstatisticwillbegreaterthan2.B)IntestsofserialcorrelationusingtheDWstatistic,thereisarejectionregion,aregionoverwhichthetestcanfailtorejectthenull,andaninconclusiveregion.C)Iftheresidualshavepositiveserialcorrelation,theDWstatistic
20、willbegreaterthan2.snpuoCJu-S-HJllpzMU-n-BJowl-ra-0Illuo4113wo3-o-BsZro-l-SS-roBpu3-ora-t-s-3-PU-ZUB-l-rol-M-roro-oro-l-l-oOUroo-ZJo-raU:MSUVModelTrendmodels1.ineartrendmodels:constantchangeamount101y=b+btLog-lineartrendmodels:constantgrowthrateIn yt =b0+ b1t + t_a(b+bt+Et)1.imitationsoftrendmodelsN
21、otappropriatewhenserialcorrelationexists.AssumptionCovariancestationaryisakeyassumptionforARtimeseriesmodeltobevalidbasedonOLSestimates.Acovariancestationaryseriesmustsatisfy:Constantandfiniteexpectedvalueinallperiods.Constantandfinitevarianceinallperiods.Constantandfinitecovariancewithitselfforafix
22、ednumberofperiodsinthepastorfutureinallperiods.-AutoregressivemodelAutoregressivemodelxt=b0blxt.1+txt三b0+b1xl+b2xt.2+.+bpxt.p+lChainruleofforecastingt=+b1xlxt+2=b0+b1xt+1AutocorrelationAutocorrelationdetectiont-testofautocorrelations(pIk)tSeasonality:showsregularpatternsofmovementwithintheyear.Testi
23、ng:t-testofseasonalautocorrelation.The4thautocorrelationincaseofquarterlydata.The12thautocorrelationincaseofmonthlydata.Correcting:includeaseasonallag.-POUJ(I)X-tro-roESI-spBMoleOUJ一Uo-S-Uo2jlUBBw-三azssalOMoPoIEUo-SSSBnbSIS3-HAJeUO-IelSoroooo-zIoU=-Ma-BMEoPUe(Io0I-UnIl-M(I)cx-l-3MUJoPUBXX-EEoPUBH_暑0
24、Hl02vu三Dickey-FullertestforunitrootStep1:startwithanAR(I)model:Xqbbt.tStep2:subtractxt.frombothsides:X辛ib(brl)xt.tOr:X辛t.fbg占ttwhere:g1=b1-lStep3:testifg=j.Hbg;H:ag割Calculatet-statisticanduserevisedcriticalvalues.IffailtorejectHthereisaunitrootandthetimeseriesisnon-stationary.FirstdifferencingArando
25、mwalk(i.e.,hasaunitroot)canbetransformedtoacovariancestationarytimeseriesbyfirstdifferencing.SubtractXt.frombothsidesofrandomwalkmodel:t-M=t-M+三t=三tDefineyqx辛心。yqendbecomecovariancestationary.QBJrmeISoUJ-0MadAl3l3pv-dEesc?Inol-0-IS=BESlllLI-MPOE一wosjSsP3enbsueoEIooHPOUJ一raEOIPoyd-O-Ep-slnoS-BnP-S一50
26、S3seu3-OJQdUJeSCOJnoPOUJ(IJE0一pod-O-EraUN-M-BnP-SBJBlIISJOtBSlSBJa-O-QHEra?c-Uo=Bn-ePOII-三azssalReliabilityvs.stabilityTheestimatesofregressioncoefficientsofthetime-seriesmodelcanchangeacrossdifferentsampleperiods.Theisatradeoffbetweenreliabilityandstability.Modelsestimatedwithshortertimeseriesareus
27、uallymorestablebutlessreliable.psnNqIoUraoUo-SSajJBU=、psuo3：IoUJn3SgJBSOMl一-psnaqCsUO-SS二BU=Eg3：MJO3n3SSOMI一-IooJInrosSE0qpcsno-IoUCraoUo-SSOJJelJOaJJBu-qoo-UnroSeils-JsE0-Uopsn-sQqUBUUO-SSeJga-JeU=Ioo-UnSBllsSE一OUoUJ-s-,lsEnOMlq-MUo-SSalmaH-ttl三BwsSaI=WlIIVBarryPhillips,CFA,isanalyzingquarterlydata
28、.HehasestimatedanAR(I)relationship(t=b0+b1xt.1+et)andwantstotestforseasonality.Todothishewouldwanttoseeifwhichofthefollowingstatisticsissignificantlydifferentfromzero?A)Correlationfeveb4)B)Correlation(et,et.1).C)Correlation(et,et.5).Answer:AAlthoughseasonalitycanmaketheothercorrelationssignificant,t
29、hefocusshouldbeoncorrelation(eet,4)becausethe4thlagisthevaluethatcorrespondstothesameseasonasthepredictedvariableintheanalysisOfquarterlydata.VsdH1.OoloIHOqITqra-rorolou8PISIoUuIVLnHoqSPIBq3leplJUJJ-PIS上JIoU(8IH,-lqSnBjqBlBPU8JEpIS上J(VE三。-ssd=三d+0+0HI+u-nsJ-0=0Spu3dzsuow-ajuroPSeUJASBsroll:OASd=IIdt-Z33=3三d
