CFA特許金融分析師-CFA二級(jí)-QuantitativeMethods

CFA特許金融分析師-CFA二級(jí)-QuantitativeMethods共享題干題AaliyahSchultzisafixed-incomeportfoliomanageratAriesI（江南博哥）nvestments.SchultzsupervisesAmerisSteele,ajunioranalyst.Afewyearsago,Schultzdevelopedaproprietarymachinelearning(ML)modelthataimstopredictdowngradesofpublicly-tradedfirmsbybondratingagencies.Themodelcurrentlyreliesonlyonstructuredfinancialdatacollectedfromdifferentsources.Schultzthinksthemodel’spredictivepowermaybeimprovedbyincorporatingsentimentdataderivedfromtextualanalysisofnewsarticlesandTwittercontentrelatingtothesubjectcompanies.SchultzandSteelemeettodiscussplansforincorporatingthesentimentdataintothemodel.TheydiscussthedifferencesinthestepsbetweenbuildingMLmodelsthatusetraditionalstructureddataandbuildingMLmodelsthatusetextualbigdata.SteeletellsSchultz:Statement1Thesecondstepinbuildingtext-basedMLmodelsistextpreparationandwrangling,whereasthesecondstepinbuildingMLmodelsusingstructureddataisdatacollection.Statement2Thefourthstepinbuildingbothtypesofmodelsencompassesdata/textexploration.SteeleexpressesconcernaboutusingTwittercontentinthemodel,notingthatresearchsuggeststhatasmuchas10%–15%ofsocialmediacontentisfromfakeaccounts.SchultztellsSteelethatsheunderstandsherconcernbutthinksthepotentialformodelimprovementoutweighstheconcern.Steelebeginsbuildingamodelthatcombinesthestructuredfinancialdataandthesentimentdata.Shestartswithcleansingandwranglingtherawstructuredfinancialdata.Exhibit1presentsasmallsampleoftherawdatasetbeforecleansing:Eachrowrepresentsdataforaparticularfirm.Aftercleansingthedata,Steelethenpreprocessesthedataset.Shecreatestwonewvariables:an“Age”variablebasedonthefirm’sIPOdateandan“InterestCoverageRatio”variableequaltoEBITdividedbyinterestexpense.Shealsodeletesthe“IPODate”variablefromthedataset.Afterapplyingthesetransformations,Steelescalesthefinancialdatausingnormalization.Shenotesthatoverthefullsampledataset,the“InterestExpense”variablerangesfromaminimumof0.2andamaximumof12.2,withameanof1.1andastandarddeviationof0.4.SteeleandSchultzthendiscusshowtopreprocesstherawtextdata.SteeletellsSchultzthattheprocesscanbecompletedinthefollowingthreesteps:Step1Cleansetherawtextdata.Step2Splitthecleanseddataintoacollectionofwordsforthemtobenormalized.Step3NormalizethecollectionofwordsfromStep2andcreateadistinctsetoftokensfromthenormalizedwords.WithrespecttoStep1,SteeletellsSchultz:“IbelieveIshouldremoveallhtmltags,punctuations,numbers,andextrawhitespacesfromthedatabeforenormalizingthem.”Afterproperlycleansingtherawtextdata,SteelecompletesSteps2and3.Shethenperformsexploratorydataanalysis.Toassistinfeatureselection,shewantstocreateavisualizationthatshowsthemostinformativewordsinthedatasetbasedontheirtermfrequency(TF)values.Aftercreatingandanalyzingthevisualization,SteeleisconcernedthatsometokensarelikelytobenoisefeaturesforMLmodeltraining;therefore,shewantstoremovethem.SteeleandSchultzdiscusstheimportanceoffeatureselectionandfeatureengineeringinMLmodeltraining.SteeletellsSchultz:“Appropriatefeatureselectionisakeyfactorinminimizingmodeloverfitting,whereasfeatureengineeringtendstopreventmodelunderfitting.”O(jiān)ncesatisfiedwiththefinalsetoffeatures,Steeleselectsandrunsamodelonthetrainingsetthatclassifiesthetextashavingpositivesentiment(Class“1”ornegativesentiment(Class“0”).Shethenevaluatesitsperformanceusingerroranalysis.TheresultingconfusionmatrixispresentedinExhibit2.[單選題]1.WhichofSteele’sstatementsrelatingtothestepsinbuildingstructureddata-basedandtext-basedMLmodelsiscorrect?A.OnlyStatement1iscorrect.B.OnlyStatement2iscorrect.C.Statement1andStatement2arecorrect.正確答案：B參考解析：Thefivestepsinbuildingstructureddata-basedMLmodelsare:1)conceptualizationofthemodelingtask,2)datacollection,3)datapreparationandwrangling,4)dataexploration,and5)modeltraining.Thefivestepsinbuildingtext-basedMLmodelsare:1)textproblemformulation,2)data(text)curation,3)textpreparationandwrangling,4)textexploration,and5)modeltraining.Statement1isincorrect:TextpreparationandwranglingisthethirdstepinbuildingtextMLmodelsandoccursaftertheseconddata(text)curationstep.Statement2iscorrect:Thefourthstepinbuildingbothtypesofmodelsencompassesdata/textexploration.[單選題]2.Steele’sconcernaboutusingTwitterdatainthemodelbestrelatesto:A.volume.B.velocity.C.veracity.正確答案：C參考解析：Veracityrelatestothecredibilityandreliabilityofdifferentdatasources.SteeleisconcernedaboutthecredibilityandreliabilityofTwittercontent,notingthatresearchsuggeststhatasmuchas10%–15%ofsocialmediacontentisfromfakeaccounts.[單選題]3.WhattypeoferrorappearstobepresentintheIPODatecolumnofExhibit1?A.invalidityerror.B.inconsistencyerror.C.non-uniformityerror.正確答案：C參考解析：Anon-uniformityerroroccurswhenthedataarenotpresentedinanidenticalformat.Thedatainthe“IPODate”columnrepresenttheIPOdateofeachfirm.WhileallrowsarepopulatedwithvaliddatesintheIPODatecolumn,thedatesarepresentedindifferentformats(e.g.,mm/dd/yyyy,dd/mm/yyyy).[單選題]4.Whattypeoferrorismostlikelypresentinthelastrowofdata(ID#4)inExhibit1?A.InconsistencyerrorB.IncompletenesserrorC.Non-uniformityerror正確答案：A參考解析：Thereappearstobeaninconsistencyerrorinthelastrow(ID#4).Aninconsistencyerroroccurswhenadatapointconflictswithcorrespondingdatapointsorreality.Inthelastrow,theinterestexpensedataitemhasavalueof1.5,andthetotaldebtitemhasavalueof0.0.Thisappearstobeanerror:Firmsthathaveinterestexpensearelikelytohavedebtintheircapitalstructure,soeithertheinterestexpenseisincorrectorthetotaldebtvalueisincorrect.Steeleshouldinvestigatethisissuebyusingalternativedatasourcestoconfirmthecorrectvaluesforthesevariables.[單選題]5.DuringthepreprocessingofthedatainExhibit1,whattypeofdatatransformationdidSteeleperformduringthedatapreprocessingstep?A.ExtractionB.ConversionC.Aggregation正確答案：A參考解析：Duringthedatapreprocessingstep,Steelecreatedanew“Age”variablebasedonthefirm’sIPOdateandthendeletedthe“IPODate”variablefromthedataset.Shealsocreatedanew“InterestCoverageRatio”variableequaltoEBITdividedbyinterestexpense.ExtractionreferstoadatatransformationwhereanewvariableisextractedfromacurrentvariableforeaseofanalyzingandusingfortraininganMLmodel,suchascreatinganagevariablefromadatevariableoraratiovariable.SteelealsoperformedaselectiontransformationbydeletingtheIPODatevariable,whichreferstodeletingthedatacolumnsthatarenotneededfortheproject.[單選題]6.BasedonExhibit1,forthefirmwithID#3,Steeleshouldcomputethescaledvalueforthe“InterestExpense”variableas:A.0.008.B.0.083.C.0.250.正確答案：B參考解析：Steeleusesnormalizationtoscalethefinancialdata.Normalizationistheprocessofrescalingnumericvariablesintherangeof[0,1].TonormalizevariableX,theminimumvalue(Xmin)issubtractedfromeachobservation(Xi),andthenthisvalueisdividedbythedifferencebetweenthemaximumandminimumvaluesofX(Xmax–Xmin):ThefirmwithID#3hasaninterestexpenseof1.2.So,itsnormalizedvalueiscalculatedas:[單選題]7.IsSteele’sstatementregardingStep1ofthepreprocessingofrawtextdatacorrect?A.Yes.B.No,becausehersuggestedtreatmentofpunctuationisincorrect.C.No,becausehersuggestedtreatmentofextrawhitespacesisincorrect.正確答案：B參考解析：Althoughmostpunctuationsarenotnecessaryfortextanalysisandshouldberemoved,somepunctuations(e.g.,percentagesigns,currencysym-bols,andquestionmarks)maybeusefulforMLmodeltraining.Suchpunctuationsshouldbesubstitutedwithannotations(e.g.,/percentSign/,/dollarSign/,and/questionMark/)topreservetheirgrammaticalmeaninginthetext.Suchannotationspreservethesemanticmeaningofimportantcharactersinthetextforfurthertextprocessingandanalysisstages.[單選題]8.Steele’sStep2canbebestdescribedas:A.tokenization.B.lemmatization.C.lemmatization.正確答案：A參考解析：Tokenizationistheprocessofsplittingagiventextintoseparatetokens.Thissteptakesplaceaftercleansingtherawtextdata(removinghtmltags,numbers,extrawhitespaces,etc.).Thetokensarethennormalizedtocreatethebag-of-words(BOW).[單選題]9.TheoutputcreatedinSteele’sStep3canbebestdescribedasa:A.bag-of-words.B.setofn-grams.C.documenttermmatrix.正確答案：A參考解析：Afterthecleansedtextisnormalized,abag-of-wordsiscreated.Abag-of-words(BOW)isacollectionofadistinctsetoftokensfromallthetextsinasampledataset.[單選題]10.Givenherobjective,thevisualizationthatSteeleshouldcreateintheexploratorydataanalysisstepisa:A.scatterplot.B.wordcloud.C.documenttermmatrix.正確答案：B參考解析：SteelewantstocreateavisualizationforSchultzthatshowsthemostinformativewordsinthedatasetbasedontheirtermfrequency(TF,theratioofthenumberoftimesagiventokenoccursinthedatasettothetotalnumberoftokensinthedataset)values.Awordcloudisacommonvisual-izationwhenworkingwithtextdataasitcanbemadetovisualizethemostinformativewordsandtheirTFvalues.Themostcommonlyoccurringwordsinthedatasetcanbeshownbyvaryingfontsize,andcolorisusedtoaddmoredimensions,suchasfrequencyandlengthofwords.[單選題]11.Toaddressherconcerninherexploratorydataanalysis,Steeleshouldfocusonthosetokensthathave:A.lowchi-squarestatistics.B.lowmutualinformation(ML)values.C.verylowandveryhightermfrequency(TF)values.正確答案：C參考解析：FrequencymeasurescanbeusedforvocabularypruningtoremovenoisefeaturesbyfilteringthetokenswithveryhighandlowTFvaluesacrossallthetexts.Noisefeaturesareboththemostfrequentandmostsparse(orrare)tokensinthedataset.Ononeend,noisefeaturescanbestopwordsthataretypicallypresentfrequentlyinallthetextsacrossthedataset.Ontheotherend,noisefeaturescanbesparsetermsthatarepresentinonlyafewtextfiles.Textclassificationinvolvesdividingtextdocumentsintoassignedclasses.ThefrequenttokensstraintheMLmodeltochooseadecisionboundaryamongthetextsasthetermsarepresentacrossallthetexts(anexampleofunderfitting).TheraretokensmisleadtheMLmodelintoclassifyingtextscontainingtheraretermsintoaspecificclass(anexampleofoverfitting).Thus,identifyingandremovingnoisefeaturesarecriticalstepsfortextclassificationapplications.[單選題]12.IsSteele’sstatementregardingtherelationshipbetweenfeatureselection/featureengineeringandmodelfitcorrect?A.Yes.B.No,becausesheisincorrectwithrespecttofeatureselection.C.No,becausesheisincorrectwithrespecttofeatureengineering.正確答案：A參考解析：Adatasetwithasmallnumberoffeaturesmaynotcarryallthecharacteristicsthatexplainrelationshipsbetweenthetargetvariableandthefeatures.Conversely,alargenumberoffeaturescancomplicatethemodelandpotentiallydistortpatternsinthedataduetolowdegreesoffreedom,causingoverfitting.Therefore,appropriatefeatureselectionisakeyfactorinminimizingsuchmodeloverfitting.Featureengineeringtendstopreventunderfittinginthetrainingofthemodel.Newfeatures,whenengineeredproperly,canelevatetheunderlyingdatapointsthatbetterexplaintheinteractionsoffeatures.Thus,featureengineeringcanbecriticaltoovercomeunderfitting.[單選題]13.BasedonExhibit2,themodel’sprecisionmetricisclosestto:A.78%.B.81%.C.81%.正確答案：A參考解析：Precision,theratioofcorrectlypredictedpositiveclasses(truepositives)toallpredictedpositiveclasses,iscalculatedas:Precision(P)=TP/(TP＋FP)=182/(182＋52)=0.7778(78%).[單選題]14.BasedonExhibit2,themodel’sF1scoreisclosestto:A.77%.B.81%.C.85%.正確答案：B參考解析：Themodel’sF1score,whichistheharmonicmeanofprecisionandrecall,iscalculatedas:F1score=(2×P×R)/(P＋R).F1score=(2×0.7778×0.8545)/(0.7778＋0.8545)=0.8143(81%).[單選題]15.BasedonExhibit2,themodel’saccuracymetricisclosestto:A.77%.B.81%.C.85%.正確答案：A參考解析：Themodel’saccuracy,whichisthepercentageofcorrectlypredictedclassesoutoftotalpredictions,iscalculatedas:Accuracy=(TP＋TN)/(TP＋FP＋TN＋FN).Accuracy=(182＋96)/(182＋52＋96＋31)=0.7701(77%).EspeyJonesisexaminingtherelationbetweenthenetprofitmargin(NPM)ofcompanies,inpercent,andtheirfixedassetturnover(FATO).Hecollectedasampleof35companiesforthemostrecentfiscalyearandfitseveraldifferentfunctionalforms,settlingonthefollowingmodel:lnNPMi=b0+b1FATOi.TheresultsofthisestimationareprovidedinExhibit1.[單選題]16.Thecoefficientofdeterminationisclosestto:A.0.0211.B.0.9789.C.0.9894.正確答案：B參考解析：Thecoefficientofdeterminationis102.9152÷105.1303=0.9789.lnNPMi=b0+b1FATOi.TheresultsofthisestimationareprovidedinExhibit1.[單選題]17.Thestandarderroroftheestimateisclosestto:A.0.2631.B.1.7849.C.38.5579正確答案：A參考解析：Thestandarderroristhesquarerootofthemeansquareerror,or√0.0692=0.2631.lnNPMi=b0+b1FATOi.TheresultsofthisestimationareprovidedinExhibit1.[單選題]18.Ata0.01levelofsignificance,Jonesshouldconcludethat:A.themeannetprofitmarginis0.5987%.B.thevariationofthefixedassetturnoverexplainsthevariationofthenaturallogofthenetprofitmargin.C.achangeinthefixedassetturnoverfrom3to4timesislikelytoresultinachangeinthenetprofitmarginof0.5987%.正確答案：B參考解析：Thep-valuecorrespondingtotheslopeislessthan0.01,sowerejectthenullhypothesisofazeroslope,concludingthatthefixedassetturnoverexplainsthenaturallogofthenetprofitmargin.lnNPMi=b0+b1FATOi.TheresultsofthisestimationareprovidedinExhibit1.[單選題]19.Thepredictednetprofitmarginforacompanywithafixedassetturnoverof2timesisclosestto:A.1.1889%.B.1.8043%.C.3.2835%正確答案：C參考解析：Thepredictednaturallogofthenetprofitmarginis0.5987＋(2×0.2951)=1.1889.Thepredictednetprofitmarginise1.1889=3.2835%.AngelaMartinez,anenergysectoranalystataninvestmentbank,isconcernedaboutthefuturelevelofoilpricesandhowitmightaffectportfoliovalues.Sheisconsideringwhethertorecommendahedgeforthebankportfolio’sexposuretochangesinoilprices.MartinezexaminesWestTexasIntermediate(WTI)monthlycrudeoilpricedata,expressedinUSdollarsperbarrel,forthe181-monthperiodfromAugust2000throughAugust2015.Theend-of-monthWTIoilpricewas$51.16inJuly2015and$42.86inAugust2015(Month181).Afterreviewingthetime-seriesdata,Martinezdeterminesthatthemeanandvarianceofthetimeseriesofoilpricesarenotconstantovertime.ShethenrunsthefollowingfourregressionsusingtheWTItime-seriesdata.Lineartrendmodel:Oilpricet=b0+b1t+etLog-lineartrendmodel:InOilpricet=b0+b1t+etAR(1)model:Oilpricet=b0+b1Oilpricet-1+etAR(2)model:Oilpricet=b0+b1Oilpricet-1+b2Oilpricet-2+etExhibit1presentsselecteddatafromallfourregressions,andExhibit2presentsselectedautocorrelationdatafromtheAR(1)models.InExhibit1,atthe5%significancelevel,thelowercriticalvaluefortheDurbin-Watsonteststatisticis1.75forboththelinearandlog-linearregressions.Afterreviewingthedataandregressionresults,Martinezdrawsthefollowingconclusions.Conclusion1:ThetimeseriesforWTIoilpricesiscovariancestationary.Conclusion2:Out-of-sampleforecastingusingtheAR(1)modelappearstobemoreaccuratethanthatoftheAR(2)model.[單選題]20.BasedonExhibit1,thepredictedWTIoilpriceforOctober2015usingthelineartrendmodelisclosestto:A.$29.15.B.$74.77.C.$103.10.正確答案：C參考解析：ThepredictedvalueforperiodtfromalineartrendiscalculatedasOctober2015isthesecondmonthoutofsample,ort=183.So,thepredictedvalueforOctober2015iscalculatedasTherefore,thepredictedWTIoilpriceforOctober2015basedonthelineartrendmodelis$103.10.Afterreviewingthetime-seriesdata,Martinezdeterminesthatthemeanandvarianceofthetimeseriesofoilpricesarenotconstantovertime.ShethenrunsthefollowingfourregressionsusingtheWTItime-seriesdata.Lineartrendmodel:Oilpricet=b0+b1t+etLog-lineartrendmodel:InOilpricet=b0+b1t+etAR(1)model:Oilpricet=b0+b1Oilpricet-1+etAR(2)model:Oilpricet=b0+b1Oilpricet-1+b2Oilpricet-2+etExhibit1presentsselecteddatafromallfourregressions,andExhibit2presentsselectedautocorrelationdatafromtheAR(1)models.InExhibit1,atthe5%significancelevel,thelowercriticalvaluefortheDurbin-Watsonteststatisticis1.75forboththelinearandlog-linearregressions.Afterreviewingthedataandregressionresults,Martinezdrawsthefollowingconclusions.Conclusion1:ThetimeseriesforWTIoilpricesiscovariancestationary.Conclusion2:Out-of-sampleforecastingusingtheAR(1)modelappearstobemoreaccuratethanthatoftheAR(2)model.[單選題]21.BasedonExhibit1,thepredictedWTIoilpriceforSeptember2015usingthelog-lineartrendmodelisclosestto:A.$29.75.B.$29.98.C.$116.50.正確答案：C參考解析：Thepredictedvalueforperiodtfromalog-lineartrendiscalculatedasSeptember2015isthefirstmonthoutofsample,ort=182.So,thepredictedvalueforSeptember2015iscalculatedasfollows:Therefore,thepredictedWTIoilpriceforSeptember2015,basedonthelog-lineartrendmodel,is$116.50.Afterreviewingthetime-seriesdata,Martinezdeterminesthatthemeanandvarianceofthetimeseriesofoilpricesarenotconstantovertime.ShethenrunsthefollowingfourregressionsusingtheWTItime-seriesdata.Lineartrendmodel:Oilpricet=b0+b1t+etLog-lineartrendmodel:InOilpricet=b0+b1t+etAR(1)model:Oilpricet=b0+b1Oilpricet-1+etAR(2)model:Oilpricet=b0+b1Oilpricet-1+b2Oilpricet-2+etExhibit1presentsselecteddatafromallfourregressions,andExhibit2presentsselectedautocorrelationdatafromtheAR(1)models.InExhibit1,atthe5%significancelevel,thelowercriticalvaluefortheDurbin-Watsonteststatisticis1.75forboththelinearandlog-linearregressions.Afterreviewingthedataandregressionresults,Martinezdrawsthefollowingconclusions.Conclusion1:ThetimeseriesforWTIoilpricesiscovariancestationary.Conclusion2:Out-of-sampleforecastingusingtheAR(1)modelappearstobemoreaccuratethanthatoftheAR(2)model.[單選題]22.BasedontheregressionoutputinExhibit1,thereisevidenceofpositiveserialcorrelationintheerrorsin:A.thelineartrendmodelbutnotthelog-lineartrendmodel.B.boththelineartrendmodelandthelog-lineartrendmodel.C.neitherthelineartrendmodelnorthelog-lineartrendmodel.正確答案：B參考解析：TheDurbin-Watsonstatisticforthelineartrendmodelis0.10andforthelog-lineartrendmodelis0.08.Bothofthesevaluesarebelowthecriticalvalueof1.75.Therefore,wecanrejectthehypothesisofnopositiveserialcorrelationintheregressionerrorsinboththelineartrendmodelandthelog-lineartrendmodel.Afterreviewingthetime-seriesdata,Martinezdeterminesthatthemeanandvarianceofthetimeseriesofoilpricesarenotconstantovertime.ShethenrunsthefollowingfourregressionsusingtheWTItime-seriesdata.Lineartrendmodel:Oilpricet=b0+b1t+etLog-lineartrendmodel:InOilpricet=b0+b1t+etAR(1)model:Oilpricet=b0+b1Oilpricet-1+etAR(2)model:Oilpricet=b0+b1Oilpricet-1+b2Oilpricet-2+etExhibit1presentsselecteddatafromallfourregressions,andExhibit2presentsselectedautocorrelationdatafromtheAR(1)models.InExhibit1,atthe5%significancelevel,thelowercriticalvaluefortheDurbin-Watsonteststatisticis1.75forboththelinearandlog-linearregressions.Afterreviewingthedataandregressionresults,Martinezdrawsthefollowingconclusions.Conclusion1:ThetimeseriesforWTIoilpricesiscovariancestationary.Conclusion2:Out-of-sampleforecastingusingtheAR(1)modelappearstobemoreaccuratethanthatoftheAR(2)model.[單選題]23.Martinez'sConclusion1is:A.correct.B.incorrectbecausethemeanandvarianceofWTIoilpricesarenotconstantovertime.C.incorrectbecausetheDurbin-WatsonstatisticoftheAR(2)modelisgreaterthan1.75.正確答案：B參考解析：Therearethreerequirementsforatimeseriestobecovariancestationary.First,theexpectedvalueofthetimeseriesmustbeconstantandfiniteinallperiods.Second,thevarianceofthetimeseriesmustbeconstantandfiniteinallperiods.Third,thecovarianceofthetimeserieswithitselfforafixednumberofperiodsinthepastorfuturemustbeconstantandfiniteinallperiods.MartinezconcludesthatthemeanandvarianceofthetimeseriesofWTIoilpricesarenotconstantovertime.Therefore,thetimeseriesisnotcovariancestationary.Afterreviewingthetime-seriesdata,Martinezdeterminesthatthemeanandvarianceofthetimeseriesofoilpricesarenotconstantovertime.ShethenrunsthefollowingfourregressionsusingtheWTItime-seriesdata.Lineartrendmodel:Oilpricet=b0+b1t+etLog-lineartrendmodel:InOilpricet=b0+b1t+etAR(1)model:Oilpricet=b0+b1Oilpricet-1+etAR(2)model:Oilpricet=b0+b1Oilpricet-1+b2Oilpricet-2+etExhibit1presentsselecteddatafromallfourregressions,andExhibit2presentsselectedautocorrelationdatafromtheAR(1)models.InExhibit1,atthe5%significancelevel,thelowercriticalvaluefortheDurbin-Watsonteststatisticis1.75forboththelinearandlog-linearregressions.Afterreviewingthedataandregressionresults,Martinezdrawsthefollowingconclusions.Conclusion1:ThetimeseriesforWTIoilpricesiscovariancestationary.Conclusion2:Out-of-sampleforecastingusingtheAR(1)modelappearstobemoreaccuratethanthatoftheAR(2)model.[單選題]24.BasedonExhibit1,theforecastedoilpriceinSeptember2015basedontheAR(2)modelisclosestto:A.$38.03.B.$40.04.C.$61.77.正確答案：B參考解析：ThelasttwoobservationsintheWTItimeseriesareJulyandAugust2015,whentheWTIoilpricewas$51.16and$42.86,respectively.Therefore,September2015representsaone-period-aheadforecast.Theone-period-aheadforecastfromanAR(2)modeliscalculatedasSo,theone-period-ahead(September2015)forecastiscalculatedasTherefore,theSeptember2015forecastbasedontheAR(2)modelis$40.04.Afterreviewingthetime-seriesdata,Martinezdeterminesthatthemeanandvarianceofthetimeseriesofoilpricesarenotconstantovertime.ShethenrunsthefollowingfourregressionsusingtheWTItime-seriesdata.Lineartrendmodel:Oilpricet=b0+b1t+etLog-lineartrendmodel:InOilpricet=b0+b1t+etAR(1)model:Oilpricet=b0+b1Oilpricet-1+etAR(2)model:Oilpricet=b0+b1Oilpricet-1+b2Oilpricet-2+etExhibit1presentsselecteddatafromallfourregressions,andExhibit2presentsselectedautocorrelationdatafromtheAR(1)models.InExhibit1,atthe5%significancelevel,thelowercriticalvaluefortheDurbin-Watsonteststatisticis1.75forboththelinearandlog-linearregressions.Afterreviewingthedataandregressionresults,Martinezdrawsthefollowingconclusions.Conclusion1:ThetimeseriesforWTIoilpricesiscovariancestationary.Conclusion2:Out-of-sampleforecastingusingtheAR(1)modelappearstobemoreaccuratethanthatoftheAR(2)model.[單選題]25.BasedonthedatafortheAR(1)modelinExhibits1and2,Martinezcanconcludethatthe:A.residualsarenotseriallycorrelated.B.autocorrelationsdonotdiffersignificantlyfromzero.C.standarderrorforeachoftheautocorrelationsis0.0745.正確答案：C參考解析：Afterreviewingthetime-seriesdata,Martinezdeterminesthatthemeanandvarianceofthetimeseriesofoilpricesarenotconstantovertime.ShethenrunsthefollowingfourregressionsusingtheWTItime-seriesdata.Lineartrendmodel:Oilpricet=b0+b1t+etLog-lineartrendmodel:InOilpricet=b0+b1t+etAR(1)model:Oilpricet=b0+b1Oilpricet-1+etAR(2)model:Oilpricet=b0+b1Oilpricet-1+b2Oilpricet-2+etExhibit1presentsselecteddatafromallfourregressions,andExhibit2presentsselectedautocorrelationdatafromtheAR(1)models.InExhibit1,atthe5%significancelevel,thelowercriticalvaluefortheDurbin-Watsonteststatisticis1.75forboththelinearandlog-linearregressions.Afterreviewingthedataandregressionresults,Martinezdrawsthefollowingconclusions.Conclusion1:ThetimeseriesforWTIoilpricesiscovariancestationary.Conclusion2:Out-of-sampleforecastingusingtheAR(1)modelappearstobemoreaccuratethanthatoftheAR(2)model.[單選題]26.Basedonthemean-revertinglevelimpliedbytheAR(1)modelregressionoutputinExhibit1,theforecastedoilpriceforSeptember2015ismostlikelytobe:A.lessthan$42.86.B.equalto$42.86.C.greaterthan$42.86.正確答案：C參考解析：Themean-revertinglevelfromtheAR(1)modeliscalculatedasTherefore,themean-revertingWTIoilpricefromtheAR(1)modelis$68.45.TheforecastedoilpriceinSeptember2015willlikelybegreaterthan$42.86becausethemodelpredictsthatthepricewillriseinthenextperiodfromtheAugust2015priceof$42.86.DorisHonoréisasecuritiesanalystwithalargewealthmanagementfirm.SheandhercolleagueBillSmithareaddressingthreeresearchtopics:howinvestmentfundcharacteristicsaffectfundtotalreturns,whetherafundratingsystemhelpspredictfundreturns,andwhetherstockandbondmarketreturnsexplainthereturnsofaportfolioofutilitysharesrunbythefirm.Toexplorethefirsttopic,HonorédecidestostudyUSmutualfundsusingasampleof555large-capUSequityfunds.Thesampleincludesfundsinstyleclassesofvalue,growth,andblend(i.e.,combiningvalueandgrowthcharacteristics).Thedependentvariableistheaverageannualizedrateofreturn(inpercent)overthepastfiveyears.Theindepe