计量经济学Test-bank-questions-Chapter-5

MultipleChoiceTestBankQuestionsNoFeedback–Chapter5Correctanswersdenotedbyanasterisk.1.Considerthefollowingmodelestimatedforatimeseriesyt=0.3+0.5yt-1-0.4t-1+twheretisazeromeanerrorprocess.Whatisthe(unconditional)meanoftheseries,yt?(a)*0.6(b)0.3(c)0.0(d)0.42.Considerthefollowingsingleexponentialsmoothingmodel:St=Xt+(1-)St-1Youaregiventhefollowingdata:ˆ=0.1,Xt=0.5,St-1=0.2IfwebelievethatthetrueDGPcanbeapproximatedbytheexponentialsmoothingmodel,whatwouldbeanappropriate2-stepaheadforecastforX?(i.e.aforecastofXt+2madeattimet)(a)0.2(b)*0.23(c)0.5(d)Thereisinsufficientinformationgiveninthequestiontoformmorethanaonestepaheadforecast.3.ConsiderthefollowingMA(3)process.yt=0.1+0.4ut-1+0.2ut-2–0.1ut-3+utWhatistheoptimalforecastforyt,3stepsintothefuture(i.e.fortimet+2ifallinformationuntiltimet-1isavailable),ifyouhavethefollowingdata?ut-1=0.3;ut-2=-0.6;ut-3=-0.3(a)0.4(b)0.0(c)*0.07(d)–0.14.Whichofthefollowingsetsofcharacteristicswouldusuallybestdescribeanautoregressiveprocessoforder3(i.e.anAR(3))?(a)*Aslowlydecayingacf,andapacfwith3significantspikes(b)Aslowlydecayingpacfandanacfwith3significantspikes(c)Aslowlydecayingacfandpacf(d)Anacfandapacfwith3significantspikes5.Aprocess,xt,whichhasaconstantmeanandvariance,andzeroautocovarianceforallnon-zerolagsisbestdescribedas(a)*Awhitenoiseprocess(b)Acovariancestationaryprocess(c)Anautocorrelatedprocess(d)Amovingaverageprocess6.WhichofthefollowingconditionsmustholdfortheautoregressivepartofanARMAmodeltobestationary?(a)*Allrootsofthecharacteristicequationmustlieoutsidetheunitcircle(b)Allrootsofthecharacteristicequationmustlieinsidetheunitcircle(c)Allrootsmustbesmallerthanunity(d)Atleastoneoftherootsmustbebiggerthanoneinabsolutevalue.7.Whichofthefollowingstatementsaretrueconcerningtime-seriesforecasting?(i)Alltime-seriesforecastingmethodsareessentiallyextrapolative.(ii)Forecastingmodelsarepronetoperformpoorlyfollowingastructuralbreakinaseries.(iii)Forecastingaccuracyoftendeclineswithpredictionhorizon.(iv)Themeansquarederrorsofforecastsareusuallyveryhighlycorrelatedwiththeprofitabilityofemployingthoseforecastsinatradingstrategy.(a)(i),(ii),(iii),and(iv)(b)*(i),(ii)and(iii)only(c)(ii),(iii)only(d)(ii)and(iv)only8.Ifaseries,yt,followsarandomwalk(withnodrift),whatistheoptimal1-stepaheadforecastfory?(a)*Thecurrentvalueofy.(b)Zero.(c)Thehistoricalunweightedaverageofy.(d)Anexponentiallyweightedaverageofpreviousvaluesofy.9.ConsideraseriesthatfollowsanMA(1)withzeromeanandamovingaveragecoefficientof0.4.Whatisthevalueoftheautocorrelationfunctionatlag1?(a)0.4(b)1(c)*0.34(d)Itisnotpossibletodeterminethevalueoftheautocovarianceswithoutknowingthedisturbancevariance.10.Whichofthefollowingstatementsaretrue?(i)AnMA(q)canbeexpressedasanAR(infinity)ifitisinvertible(ii)AnAR(p)canbewrittenasanMA(infinity)ifitisstationary(iii)The(unconditional)meanofanARMAprocesswilldependonlyontheinterceptandontheARcoefficientsandnotontheMAcoefficients(iv)Arandomwalkserieswillhavezeropacfexceptatlag1(a)(ii)and(iv)only(b)(i)and(iii)only(c)(i),(ii),and(iii)only(d)*(i),(ii),(iii),and(iv).11.Considerthefollowingpictureandsuggestthemodelfromthefollowinglistthatbestcharacterisestheprocess:-0.100.10.20.30.40.50.60.70.80.912345678910Lagsacfandpacfacfpacf(a)AnAR(1)(b)AnAR(2)(c)*AnARMA(1,1)(d)AnMA(3)Theacfisclearlydecliningveryslowlyinthiscase,whichisconsistentwiththeirbeinganautoregressiveparttotheappropriatemodel.Thepacfisclearlysignificantforlagsoneandtwo,butthequestionisdoesitthembecomeinsignificantforlags2and4,indicatinganAR(2)process,ordoesitremainsignificant,whichwouldbemoreconsistentwithamixedARMAprocess?Well,giventhehugesizeofthesamplethatgaverisetothisacfandpacf,evenapacfvalueof0.001wouldstillbestatisticallysignificant.ThusanARMAprocessisthemostlikelycandidate,althoughnotethatitwouldnotbepossibletotellfromtheacfandpacfwhichmodelfromtheARMAfamilywasmoreappropriate.TheDGPforthedatathatgeneratedthisplotwasy_t=0.9y_(t-1)–0.3u_(t-1)+u_t.12.Whichofthefollowingmodelscanbeestimatedusingordinaryleastsquares?(i)AnAR(1)(ii)AnARMA(2,0)(iii)AnMA(1)(iv)AnARMA(1,1)(a)(i)only(b)*(i)and(ii)only(c)(i),(ii),and(iii)only(d)(i),(ii),(iii),and(iv).13.Ifaseries,y,isdescribedas“mean-reverting”,whichmodelfromthefollowinglistislikelytoproducethebestlong-termforecastsforthatseriesy?(a)Arandomwalk(b)*Thelongtermmeanoftheseries(c)AmodelfromtheARMAfamily(d)Arandomwalkwithdrift14.ConsiderthefollowingAR(2)model.Whatistheoptimal2-stepaheadforecastforyifallinformationavailableisuptoandincludingtimet,ifthevaluesofyattimet,t-1andt-2are–0.3,0.4and–0.1respectively,andthevalueofuattimet-1is0.3?yt=-0.1+0.75yt-1-0.125yt-2+ut(a)-0.1(b)0.27(c)*-0.34(d)0.3015.Whatistheoptimalthree-stepaheadforecastfromtheAR(2)modelgiveninquestion14?(a)-0.1(b)0.27(c)-0.34(d)*-0.3116.Supposeyouhadtoguessatthemostlikelyvalueofaonehundredstep-aheadforecastfortheAR(2)modelgiveninquestion14–whatwouldyourforecastbe?(a)-0.1(b)0.7(c)*–0.27(d)0.75