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BusinessandEconomicForecastingChapter5DemandForecastingisacriticalmanagerialactivitywhichcomesintwoforms:QualitativeForecastingGivesth

eExpectedDirectionQuantitativeForecastingGivesthepreciseAmount2.7654%©2002South-WesternPublishingTime-SeriesCharacteristics:Secu

larTrendandCyclicalVariationinWomen’sClothingSalesTime-SeriesCharacteristics:SeasonalPatternandRandomFluctuationsMicrosoftCorp.Sal

esRevenue,1984–2001Figure6.2WhiteNoiseandMA(1)TimeSeries-1.5-1-0.500.511.5135791113151719212325272931333537394143454749Whi

teNoiseMA(1)AMA(1)Process⚫Amovingaverageprocessoforderone[MA(1)]canbecharacterizedasonewherext=et+a1et-1,

t=1,2,…withetbeinganiidsequencewithmean0andvariance⚫Thisisastationary,weaklydependentsequenceasvariables1periodapartarecorrelated,but2periodsapartthe

yarenot2eThreeStationaryAR(1)TimeSeries-3.5-2.5-1.5-0.50.51.5135791113151719212325272931333537394143454749rho=.1rho=.5rho=.90AnAR(1)Process⚫An

autoregressiveprocessoforderone[AR(1)]canbecharacterizedasonewhereyt=ρyt-1+et,t=1,2,…withetbeinganiidsequencewithmean0andvarianceσ2Forthisprocesstob

eweaklydependent,itmustbethecasethat|ρ|<1⚫Corr(yt,yt+h)=Cov(yt,yt+h)/(σyσy)=ρ1hwhichbecomessmallashincreasesThreeStationaryAR(1)

TimeSeries−1-4-3-2-101234135791113151719212325272931333537394143454749rho=-.1rho=-.5rho=-.9StationaryStochasticProcess⚫Astoc

hasticprocessisstationaryifforeverycollectionoftimeindices1≤t1<…<tmthejointdistributionof(xt1,…,xtm)isthesameasthatof(xt1+h,…xtm+h)forh≥1⚫Thu

s,stationarityimpliesthatthext’sareidenticallydistributedandthatthenatureofanycorrelationbetweenadjacenttermsisthesameacrossallperiodsCovarianceStat

ionaryProcess⚫AstochasticprocessiscovariancestationaryifE(xt)isconstant,Var(xt)isconstantandforanyt,h≥1,Cov(xt,xt+h)dependsonlyonhandnotont⚫Thu

s,thisweakerformofstationarityrequiresonlythatthemeanandvarianceareconstantacrosstime,andthecovariancejustd

ependsonthedistanceacrosstimeThreeNon-StationaryAR(1)TimeSeries-30-25-20-15-10-50510152013579111315171921232527293133353739rho=

1rho=1.25rho=-1.25ARandomWalkandARandomWalkWithDrift-6-4-202468135791113151719212325272931333537394143454749RandomWa

lkRandomWalkWithDriftRandomWalks⚫ArandomwalkisanAR(1)modelwhereρ1=1,meaningtheseriesisnotweaklydependent⚫Witharandomwalk,theexpectedvalueofyt

isalwaysy0–itdoesn’tdependont⚫Var(yt)=σet,soitincreaseswitht⚫WesayarandomwalkishighlypersistentsinceE(y

t+h|yt)=ytforallh≥1RandomWalks(continued)⚫Arandomwalkisaspecialcaseofwhat’sknownasaunitrootprocess⚫Notethattrendingandpersiste

ncearedifferentthings–aseriescanbetrendingbutweaklydependent,oraseriescanbehighlypersistentwithoutanytrend⚫Arandomwalkwi

thdriftisanexampleofahighlypersistentseriesthatistrendingRandomWalkwithDriftvs.TrendStationaryAR(1)-3-11357911135

791113151719212325272931333537394143454749RandomWalkWithDriftTrendStationaryAR(1)TrendingTimeSeries⚫Economictimeseriesoftenhaveatrend⚫Justbecause2se

riesaretrendingtogether,wecan’tassumethattherelationiscausal⚫Often,bothwillbetrendingbecauseofotherunobservedf

actors⚫Evenifthosefactorsareunobserved,wecancontrolforthembydirectlycontrollingforthetrend⚫Atrendingseriescannotbest

ationary,sincethemeanischangingovertime⚫Atrendingseriescanbeweaklydependent⚫Ifaseriesisweaklydependentandisstationa

ryaboutitstrend,wewillcallitatrend-stationaryprocessDetrending⚫Addingalineartrendtermtoaregressionisthesamethingasusing“de

trended”seriesinaregression⚫Detrendingaseriesinvolvesregressingeachvariableinthemodelont⚫Theresidualsfor

mthedetrendedseries⚫Basically,thetrendhasbeenpartialledoutWhyForecastDemand?⚫Bothpublicandprivateenterprisesoperateunderconditionsofuncertain

ty.⚫Managementwishestolimitthisuncertaintybypredictingchangesincost,price,sales,andinterestrates.⚫Accurateforecastingcanhelpdevelopstrategie

stopromoteprofitabletrendsandtoavoidunprofitableones.⚫Aforecastisapredictionconcerningthefuture.Goodforecastingwillredu

ce,butnoteliminate,theuncertaintythatallmanagersfeel.HierarchyofForecasting⚫Theselectionofforecastingtechniquesdependsinpartonthelevelofeconomicag

gregationinvolved.Thehierarchyofforecastingis:⚫NationalEconomy(GDP,interestrates,inflation,etc.)sectorsoftheeconomy

(durablegoods)industryforecasts(automobilemanufacturers)•firmforecasts(FordMotorCompany)ForecastingCriteriaThechoiceofaparticularforecastingmethod

dependsonseveralcriteria:⚫costsoftheforecastingmethodcomparedwithitsgains⚫complexityoftherelationshipsamongvariables⚫timeperiodinvo

lved⚫accuracyneededinforecast⚫theleadtimebetweenreceivinginformationandthedecisiontobemadeSignificanceofForecasti

ng⚫Theaccuracyofaforecastingmodelismeasuredbyhowclosetheactualvariable,Y,endsuptotheforecastingvariable,Y.⚫Forecasterroristhedifference.(

Y-Y)⚫Modelsdifferinaccuracy,whichisoftenbasedonthesquarerootoftheaveragesquaredforecasterroroveraseriesofNforecas

tsandactualfigures⚫Calledarootmeansquareerror,RMSE.RMSE={(Y-Y)2/N}^^^QualitativeForecasting⚫Flexibility--easilyalteredaseconomychanges⚫Ea

rlySignals--cancatchchangesandanomaliesindata⚫Complex--hardtokeeptrackofinteractionsintheprimaryvariables⚫LackofTestsforAccuracy-

-can’teasilytesttheaccuracyinpriorperiods.ADVANTAGESLIMITATIONSAdvantagesOrganizerelationshipsBehaviora

lrelationshipsTestsofreliabilityQuantitativeForecastingandtheUseofModelsLimitationsEconomychangesDataminingofsameinformati

onOnlyacrudeapproximation“Economicforecastingisreallytheartofidentifyingtensionsorimbalancesintheeconomicprocessandunderstandinginwhatmannerthe

ywillberesolved.”-A.GreenspanIseeaTroubleaheadAlanGreenspan--ChairmanoftheBoardofGovernorsoftheFederalReserveQualitativeForeca

sting1.ComparativeStaticsShiftsinDemandShiftsinSupplyForecastChangesinPricesandQuantities⚫SupposeI

ncomeShiftsPriceRisesQuantityRisesquantityPsupplyD1D2AB2.ExpertOpinionTheaverageforecastfromseveralexpertsisaConsensusForecast.MeanMedianModeP

ercentilesQuartilesExample:ApartmentRentsGivenbelowisasampleofmonthlyrentvalues($)forone-bedroomapartments.Theda

taisasampleof70apartmentsinaparticularcity.Thedataarepresentedinascendingorder.425430430435435435435435440440440440440445445

4454454454504504504504504504504604604604654654654704704724754754754804804804804854904904905005005005005105105155255255255355495505705

70575575580590600600600600615615Mean⚫Themeanofadatasetistheaverageofallthedatavalues.⚫Ifthedataarefromasample,themeanisdenotedby⚫Ifthed

ataarefromapopulation,themeanisdenotedbym(mu).xxni==xNiExample:ApartmentRents⚫Mean4254304304354354354354354404404

4044044044544544544544545045045045045045045046046046046546546547047047247547547548048048048048549049049050050050050051

0510515525525525535549550570570575575580590600600600600615615xxni===343567049080,.Median⚫Themedianist

hemeasureoflocationmostoftenreportedforannualincomeandpropertyvaluedata.⚫Afewextremelylargeincomesorpropertyvaluesca

ninflatethemean.Median⚫Themedianofadatasetisthevalueinthemiddlewhenthedataitemsarearrangedinascendingorder.⚫Foranoddnumberof

observations,themedianisthemiddlevalue.⚫Foranevennumberofobservations,themedianistheaverageofthetwomiddlevalues.Example:ApartmentRentsMedian=50thpe

rcentilei=(p/100)n=(50/100)70=35.5Averagingthe35thand36thdatavalues:Median=(475+475)/2=47542543043043543543543543544044044044044044544

54454454454504504504504504504504604604604654654654704704724754754754804804804804854904904905005005005005105105155255255255355

49550570570575575580590600600600600615615Mode⚫Themodeofadatasetisthevaluethatoccurswithgreatestfrequency.⚫Thegreatestfrequencycano

ccurattwoormoredifferentvalues.⚫Ifthedatahaveexactlytwomodes,thedataarebimodal.⚫Ifthedatahavemorethantwomodes,thedat

aaremultimodal.Example:ApartmentRents450occurredmostfrequently(7times)Mode=45042543043043543543543543544044

044044044044544544544544545045045045045045045046046046046546546547047047247547547548048048048048549049

0490500500500500510510515525525525535549550570570575575580590600600600600615615Percentiles⚫Apercentileprovidesinfo

rmationabouthowthedataarespreadovertheintervalfromthesmallestvaluetothelargestvalue.⚫Admissiontestscoresforcollegesanduniversitiesarefrequentlyr

eportedintermsofpercentiles.PercentilesThepthpercentileofadatasetisavaluesuchthatatleastppercentoftheitemstakeonthisvalu

eorlessandatleast(100-p)percentoftheitemstakeonthisvalueormore.Arrangethedatainascendingorder.Computeindexi,thepositionofthepthpercentile.i=(

p/100)nIfiisnotaninteger,roundup.Thepthpercentileisthevalueintheithposition.Ifiisaninteger,thepthpercentileistheaverageo

fthevaluesinpositionsiandi+1.Example:ApartmentRents⚫90thPercentilei=(p/100)n=(90/100)70=63Averagingthe63rdand64thdatavalues:90thPercentile=(580+590

)/2=585425430430435435435435435440440440440440445445445445445450450450450450450450460460460465465465470470472475475475

480480480480485490490490500500500500510510515525525525535549550570570575575580590600600600600615615Quartiles⚫Q

uartilesarespecificpercentiles⚫FirstQuartile=25thPercentile⚫SecondQuartile=50thPercentile=Median⚫Thi

rdQuartile=75thPercentileExample:ApartmentRents⚫ThirdQuartileThirdquartile=75thpercentilei=(p/100)n=(75/100)70=52.5=53Thirdquartile=52542543043043

5435435435435440440440440440445445445445445450450450450450450450460460460465465465470470472475475475480480480480485

490490490500500500500510510515525525525535549550570570575575580590600600600600615615EXAMPLES:•IBESandZacksInvestment--earningsforecastsofstockanal

ysts•ConferenceBoard--macroeconomicpredictions•LivingstonSurveys--macroeconomicforecastsof50-60economists•DelphiTechnique--panelofdiverseexp

erts.1.Writeoutforecasts2.Showthemtootherpanelists3.meettoarriveatconsensusNote:problemsofexpenseandintransigenceDelphiapproachTheDelphim

ethodrecognizeshumanjudgmentaslegitimateandusefulinputsingeneratingforecasts.Singleexpertssometimessufferbiases;groupmeetingssufferfrom"fo

llowtheleader"tendenciesandreluctancetoabandonpreviouslystatedopinions(GatewoodandGatewood,1983,Fowles,1978).Inordertoovercomethesesh

ortcomingsthebasicnotionoftheDelphimethod,theoreticalassumptionsandmethodologicalproceduresdevelopedinthe1950san

d1960sattheRANDCorporation.Forecastsaboutvariousaspectofthefutureareoftenderivedthroughthecollationofexpertjudgment.⚫Fowles(1

978)describesthefollowingtenstepsfortheDelphimethod:⚫FormationofateamtoundertakeandmonitoraDelphionagi

vensubject;⚫Selectionofoneormorepanelstoparticipateintheexercise.Customarily,thepanelistsareexpertsintheareatobeinvestigated;⚫Developmentofthefir

stroundDelphiquestionnaire;⚫Testingthequestionnaireforproperwording(e.g.,ambiguities,vagueness);⚫Transmissionofthef

irstquestionnairestothepanelists;⚫Analysisofthefirstroundresponses;⚫Preparationofthesecondroundquestionnaires(andpossibletesting);⚫Transmissionofthe

secondroundquestionnairestothepanelists;⚫Analysisofthesecondroundresponses(Steps7to9arereiteratedaslongasd

esiredornecessarytoachievestabilityintheresults);⚫Preparationofareportbytheanalysisteamtopresenttheco

nclusionsoftheexercise.3.Surveys⚫Samplebias--telephone,magazine⚫Biasedquestions--advocacysurveys⚫Ambi

guousquestions⚫RespondentsmaylieonquestionnairesNewProductshavenohistoricaldata--Surveyscanassessinterestinnewideas.Survey

ResearchCenterofU.ofMich.doesrepeatsurveysofhouseholdsonBigTicketitems(Autos)CommonSurveyProblemsDirectionof

salescanbeindicatedbyothervariables.TIMEIndexofCapitalGoodspeakPEAKMotorControlSales4MonthsExample:IndexofCapitalGoodsisa“le

adingindicator”Therearealsolaggingindicatorsandcoincidentindicators4.EconomicIndicators(BarometricForecasting)LEADINGINDICATORS*M2

moneysupply(-10.9)S&P500stockprices(-6.9)Newhousingpermits(-10.1)Initialunemploymentclaims(-7.3)Orders

forplantandequipment(-3.9)COINCIDENTINDICATORSNonagriculturalemployment(+.9)Indexofindustrialproduction(-.6)Personalincomelesstr

ansferpayment(-.6)LAGGINGINDICATORSPrimerate(+12.2)Durationofunemployment(+4.4)TimegiveninmonthsfromchangeQuestio

nsWhyarecontractsandordersforplantandequipmentappropriateleadingindicators?Whyistheindexofindustrialproductionanappropriatecoincide

ntindicator?Whyistheprimerateanappropriatelaggingindicator?ExamplesofIndicatorsCompositeExample:Oneindicatorrises4%andanotherrises6%TheCompositeIndex

isa5%increase.DiffusionExample:WallStreetWeekwithelevenanalysts,where4arenegativeaboutstocksand7arepositive:TheDiffusionIndexi

s7/11,or63.3%.InterpretingandUsingIndices⚫compositeindex-weightedaverageindexofindividualindicatorsindexinterpretedintermsof%changecompositeindexo

fleadingeconomicindicators:sustainedincreaseindicateseconomicgrowth⚫diffusionindex-measureoftheproportionofindividualtimeseri

esthatincreasefordiffusionindexofleadingeconomicindicators,ifindex>50%,improvedconditionsareexpectedWhatWentWrongWi

thSUVsatFordMotorCo?⚫ChryslerintroducedtheMinivaninthe1980’s⚫FordexpandeditscapacitytoproducetheExplorer,itspopularSUV⚫Explorer’spriceraisedin199

5substantiallyatsametimeasChrysler’sJeepCherokeeandGMexpandeditsChevroletSUV⚫Mustconsiderresponseofrivalsinpr

icingdecisionsQuantitativeForecasting⚫TimeSeriesLooksForPatternsOrderedbyTimeNoUnderlyingStructure⚫EconometricModelsExplainsrelationships

Supply&DemandRegressionModelsLiketechnicalsecurityanalysisLikefundamentalsecurityanalysisTimeSeriesExaminePatternsinthePastTIMEToXXXDependent

Variable⚫TimeSeriesisaquantitativeforecastingmethodUsespastdatatoprojectthefuturelooksforhighestACCURACYpossible⚫Accuracy(MSE&MAD)MeanSquaredError&Me

anAbsoluteDeviation⚫Ft+1=f(At,At-1,At-2,...)LetF=forecastandLetA=actualdataMSE=t=1[Ft-At]2/NTheLOWERtheMSEorMAD,thegreatertheaccuracyMAD=t=1|(F

t-At)|/NMethodsofTimeSeriesAnalysisforEconomicForecasting1.NaiveForecastFt+1=AtMethodbestwhenthereisnotrend,onlyrandomerrorGraphso

fsalesovertimewithandwithouttrendsNOTrendTrend2.MovingAverage⚫Asmoothingforecastmethodfordatathatjumpsaround⚫Bestwhenthereisnotrend⚫3-PeriodMo

vingAve.Ft+1=[At+At-1+At-2]/3*****ForecastLineTIMEDependentVariable3.ExponentialSmoothing⚫AhybridoftheNaiveandMovingAveragemethods⚫F

t+1=.•At+(1-)Ft⚫Aweightedaverageofpastactualandpastforecast.⚫Eachforecastisafunctionofallpastobservations⚫Canshowt

hatforecastisbasedongeometricallydecliningweights.Ft+1=.•At+(1-)••At-1+(1-)2••At-1+…FindlowestMSEtopickthebe

stalpha.4.Linear&5.Semi-log⚫UsedwhentrendhasaconstantAMOUNTofchangeAt=a+b•T,whereAtaretheactualobservationsandTisanumer

icaltimevariable⚫UsedwhentrendisaconstantPERCENTAGErateLogAt=a+b•T,wherebisthecontinuouslycompoundedgrowthrateLin

earTrendRegressionSemi-logRegressionMoreonSemi-logFormaproof⚫Suppose:Salest=Sales0(1+G)twhereGistheannualgrowthrate

⚫Takethenaturallogofbothsides:LnSt=LnS0+t•Ln(1+G)butLn(1+G)=g,theequivalentcontinuouslycompoundedgr

owthrateSO:LnSt=LnS0+t•gLnSt=a+g•tNumericalExamples:6observationsMTB>Printc1-c3.SalesTimeLn-sales100.014.60517109.824.69866121.634.800

74133.744.89560146.254.98498164.365.10169Usingthissalesdata,estimatesalesinperiod7usingalinearandasemi-logfunctionalform

TheregressionequationisSales=85.0+12.7TimePredictorCoefStdevt-ratiopConstant84.9872.41735.160.000Time12.65140.620720

.380.000s=2.596R-sq=99.0%R-sq(adj)=98.8%TheregressionequationisLn-sales=4.50+0.0982TimePredictorCoefStdevt-ratiopC

onstant4.504160.00642701.350.000Time0.0981830.00164959.540.000s=0.006899R-sq=99.9%R-sq(adj)=99.9%ForecastedSales@Time=7⚫LinearModel⚫Sales=8

5.0+12.7Time⚫Sales=85.0+12.7(7)⚫Sales=173.9⚫Semi-LogModel⚫Ln-sales=4.50+0.0982Time⚫Ln-sales=4.50+0.0982(7)⚫Ln-sales=5.1874⚫Toanti-log:e5.1874=179.0

linearSalesTimeLn-sales100.014.60517109.824.69866121.634.80074133.744.89560146.254.98498164.365.10169179.0

7semi-log173.97linearWhichpredictiondoyouprefer?Semi-logisexponential76.ProceduresforSeasonalAdjustments⚫TakeratiosofA/Fforpasty

ears.Findtheaverageratio.AdjustbythispercentageIfaverageratiois1.02,adjustforecastupward2%⚫UseDummyVariablesinaregression:D=1if4thquarter;0o

therwise12-quartersofdataIIIIIIIVIIIIIIIVIIIIIIIVQuartersdesignatedwithromannumerals.DummyVariablesforSeasonalAdjustments⚫LetD=1,if4thquarteran

d0otherwise⚫Runanewregression:At=a+b•T+c•Dthe“c”coefficientgivestheamountoftheadjustmentforthefourthqu

arter.ItisanInterceptShifter.⚫EXAMPLE:Sales=300+10•T+18•D12Observations,1999-Ito2001-IV,Forecastallof2002.Sales(200

2-I)=430;Sales(2002-II)=440;Sales(2002-III)=450;Sales(2002-IV)=478DummyVariableInteractions⚫Canintroduceaslopeshi

fterby“interacting”twovariablesAt=a+b•T+c•D+d•D•Tcistheinterceptshifterdistheslopeshifter⚫E.g.,Sales=300+10•T+18•D-3•D•Timpli

esthattheInterceptis318,whenD=1impliesthattheslopeis7,whenD=1EconometricModels⚫Specifythevariablesinthemodel⚫Estimateth

eparameterssingleequationorperhapsseveralstagemethodsQd=a+b•P+c•I+d•Ps+e•Pc⚫Butforecastsrequireestimatesforfutureprices,futureincome

,etc.⚫Oftencombineeconometricmodelswithtimeseriesestimatesoftheindependentvariable.GarbageinGarbageoutexample⚫Qd=400-.5•P+2•Y+.2•Psant

icipatepricingthegoodatP=$20Incomeisgrowingovertime,theestimateis:LnYt=2.4+.03•T,andnextperiodisT=17.Thepricesofsubstitutesar

elikelytobeP=$18.⚫FindQd⚫Y=e2.910=18.357⚫HenceQd=430.31