品職教育2017年cfa二級quant知識框架圖何旋版

CFA二級知識框架FrameworkofCFA tativeCorrelationandMultipleRegressionandIssuesIn Time-Time-Time- ysis,DecisionTrees,Reading H0:ρ=0;t-

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t= n-2,df=n-

-t

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SimpleLinear建ANOVA建ANOVATable分檢驗?zāi)ｎA(yù)

Yib0b1Xii,i1,..., inedvariable,predicted natoryvariable,predicting★①②③④⑤⑥AlinearrelationshipexistsbetweenXandXisuncorrelatedwiththeerrorTheexpectedvalueoftheerrortermiszero(i.e.,E(εi)=0ThevarianceoftheerrortermisconstantTheerrortermisuncorrelatedacrossobservations(E(εiεj)=0forTheerrortermisnormallyAnestimatedslopecoefficientof2：Ywillchangetwounitsforevery1unitchangeinCoefficient估Intercepttermof2%：theXiszero,Yis★bCov(X,YbYb計 Var(X n-k-MSE=SSE/(n-k-n--計算 R2SSR1 R2 (多元都成立R2(一元解釋：R2of0.90indicatesthatthevariationoftheindependentvariableins90%ofvariationinthedependent計算 SEE nk性質(zhì)TheSEEgaugesthe“fit”oftheregressionline.Thesmallerthestandarderror,thebettertheTheSEEisthestandarddeviationoftheerrortermsinthe考試時考試時給定條t-p-0s?b？1s1？分?t t:查 c AsSEErises,sb?also1t? sDecisionrule:rejectH0if+tcritical<t,ort<-tRejectionofthenullmeansthattheslopecoefficientisdifferentfrom?? Y?tcsf 了WhenWhenpredictingYusinglinearregressionmodel,weencountertwotypesofUncertaintyintheregressionmodelitself,asreflectedinthestandarderrorofUncertaintyabouttheestimatesoftheregressionmodel’sReadingMULTIPLEREGRESSIONANDISSUESIN MultipleRegression&SimpleLinear

要EachslopecoefficientistheestimatedchangeinYforaoneunitchangeinXi,holdingtheb?bs單個檢 t sSignificance

df=n-k-聯(lián)合檢驗(F-test)：Thetestassessestheeffectivenessofthemodelasawholeinex dependentvariableH0:b1=b2=b3=…= MSR SSR Ha:atleastonebj≠0(j=1torejectH0:ifF(test-statistic)>Fc(criticalTheF-testhereisalwaysaone-tailed

FMSE

SSE(nk1)yststypicallydonotuseANOVAandF-testsinsimplelinearregressionbecausethestatisticisthesquareofthet-statisticfortheslopeMultipleRegression&SimpleLinearRegression要解釋：R2of0.90indicatesthatthemodelasawholeins90%ofthevariationin缺點：R2almostalwaysincreasesasvariablesareaddedtothemodel,evenifthecontributionofthenewvariablesisnotstatisticallyn1 (計算)AdjustedR2：adjustedR2 nk SSTnR2R2YMultipleMultipleRegressionAssumptionUnconditional:nomajorConditional:significantNotaffecttheconsistencyofparameterCoefficientestimatesarenotStandarderrorsareusuallyunreliabletoosmall—>TypeIBreuschnχ2H0:NoBP=n×Rresidual2,df=k,one-tailedgeneralizedleastRejectH0,positiveRejectH0,positiveserialnotrejectRejectH0,negativeserialSerialCorrelationSerialcorrelationisoftenfoundintimeseriesNotaffecttheconsistencyofestimatedregressioncoefficientsandcoefficientPositiveserialcorrelationismuchmorecommon:Positiveserialcorrelation→standarderrorsthataretoosmall→TypeIerror&F-testDurbin-Watsontest(看下圖H0Noserialcorrelation,DW 4- 4- adjustingthecoefficientstandarderrors(e.g.,Hansenmethod):theHansenmethodalsoincorporatethetime-seriesThesituationthattwoormoreindependentvariablesarehighly(butperfectly)correlatedwitheachNotaffecttheconsistencyofregressioncoefficient eextremelyimpreciseandImpossibletodistinguishtheindividualimpactsoftheindependent①t-testsindicatethatnoneoftheindividualcoefficientsissignificantlydifferentthanzero,whiletheF-testindicatesoverallsignificanceandtheR2ishigh②︱rX1X2︱Removeoneormoreindependent模Qualitativevariable：0andncategories→n?1dummy例：EPStb0b1Q1tb2Q2tb3Q3tEPSt=aquarterlyobservationofearningsperQ1t=1ifperiodtisthefirstquarter,Q1t=0Q2t=1ifperiodtisthesecondquarter,Q2t=0Q3t=1ifperiodtisthethirdquarter,Q3t=0b0：averagevalueofEPSfor Slopecoefficient：differenceinEPS(onaverage)betweentherespective(i.e.,quarter1,2,or3)andtheomitted比如，b1EPS1①ThefunctionalformcanbeImportantvariablesareVariablesshouldbeDataisimproperly②TimeseriesAlaggedYisusedasanXwithseriallycorrelatedAfunctionoftheYisusedasanX(forecastingtheIndependentvariablesaremeasuredwith③Time-seriesdata:ModelReadingTIME- Log-linearLog-lineartrendmodel:Ln(yt)Ifthedataplotswithanon-linear(curved)shape,thentheresidualsfromatrendmodelwillbepersistentlypositiveornegativeforaperiodof每期的增長率是constantTrendLineartrend:Thedatapointsappeartobeequallydistributedaboveandbelowtheregression每期增長量是constant使用trend

以AR(1)開始模型的估ARARPxtb0b1xt1b2xt2...bpxtpARChainruleof xt1b0b1 計Assumption具體看后面NoNoConditionalCovariance-stationary檢驗是否有Seasonality(具體看后面)+(CompareforecastingsmallestRMSEforout-of-sample→最 RMSE計ARARModel考試時給的表1、Noautocorrelation:針對考試時給的表H: No t tstatistics t standarderror1/ RejectH0:t>+tcritical,ort<-tRejectH0:(addlaggedvalues)AR(1)→H: H: No tRejectH0:t>+tcritical,ort<-t2、NoConditionalHeteroskedasticity:針對residualterm(用含HeteroskedasticityreferstothesituationthatthevarianceoftheerrortermisnotTestConditionalHeteroskedasticity=Testwhetheratimeseriesis2aa 1t a1issignificantlydifferentfrom0→ConditionalHeteroskedasticityGeneralizedleastCovariance- Constantandfiniteexpectedvalueofthetime ConstantandfinitevarianceofthetimeCovariance- Constantandfiniteexpectedvalueofthetime Constantandfinitevarianceofthetime ConstantandfinitecovariancewithleadingorlaggedMeanMean-reverting:11xt>mean—>xt+1<xxt<mean—>xt+1>x含含相SimpleSimplerandomwalk:xt=xt-Randomwalkwithadrift:xt=b0+b1xt-1+εtunitRandomxtxt=b0+b1xt-1+εt→xt-xt-1=b0+gxt-1+εt(g=b1H0:g=0(hasaunitrootandisnonstationary);Ha:RejectH0→thetimeseriesdoesnothaveaunitrootandis檢Defineytasyt=xt-xt-1→AR(1)modelyt=b0+b1yt-1First修Ytb0 RegressionwithMoreThanOneTimeNoneofthetimeserieshasaunit?Atleastonetimeserieshasaunitrootwhileatleastonetimeseriesdoes?Eachtimeserieshasaunitroot:whetherthetimeseriesarecointegrated??no?IfIfwecannotrejectthenull,wecannotusemultipleIfwecanrejectthenull,wecanusemultipleHa:H0:noTestthecointegration:Dickey-FullerEngle-Grangertest(DF-EGReading YSIS,DECISIONTREE,ANDSelective&full TypeofCorrelationacross

ysis:Selective Decisiontreesandsimulations:full Decisiontrees:amanageablesetof Simul