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BusinessandEconomicForecastingChapter5DemandForecastingisacriticalmanagerialactivitywhichcomesintwoforms:QualitativeForecastingGivestheExpectedDir

ectionQuantitativeForecastingGivesthepreciseAmount2.7654%©2002South-WesternPublishingTime-SeriesCharacteristics:SecularTrendandCycli

calVariationinWomen’sClothingSalesTime-SeriesCharacteristics:SeasonalPatternandRandomFluctuationsMicrosoftCorp

.SalesRevenue,1984–2001Figure6.2WhiteNoiseandMA(1)TimeSeries-1.5-1-0.500.511.5135791113151719212325272

931333537394143454749WhiteNoiseMA(1)AMA(1)Process⚫Amovingaverageprocessoforderone[MA(1)]canbecharacterizedasonewherext=et+a1et-1,t=1,2,…withetbei

nganiidsequencewithmean0andvariance⚫Thisisastationary,weaklydependentsequenceasvariables1periodapartarecorrelated,but2periodsaparttheyarenot2eThree

StationaryAR(1)TimeSeries-3.5-2.5-1.5-0.50.51.5135791113151719212325272931333537394143454749rho=.1rho=.5rho=.90AnAR(1)Process⚫Anauto

regressiveprocessoforderone[AR(1)]canbecharacterizedasonewhereyt=ρyt-1+et,t=1,2,…withetbeinganiidsequencewithmean0andv

arianceσ2Forthisprocesstobeweaklydependent,itmustbethecasethat|ρ|<1⚫Corr(yt,yt+h)=Cov(yt,yt+h)/(σyσy)=ρ1hwhichbecomessmallashincreasesThreeStatio

naryAR(1)TimeSeries−1-4-3-2-101234135791113151719212325272931333537394143454749rho=-.1rho=-.5rho=-.9StationaryStoc

hasticProcess⚫Astochasticprocessisstationaryifforeverycollectionoftimeindices1≤t1<…<tmthejointdistributionof(xt1,…,xtm)isthesameasthatof(xt1+h,…xtm

+h)forh≥1⚫Thus,stationarityimpliesthatthext’sareidenticallydistributedandthatthenatureofanycorrelationbe

tweenadjacenttermsisthesameacrossallperiodsCovarianceStationaryProcess⚫AstochasticprocessiscovariancestationaryifE(xt)isconstant,Var(

xt)isconstantandforanyt,h≥1,Cov(xt,xt+h)dependsonlyonhandnotont⚫Thus,thisweakerformofstationarityrequiresonlythatthem

eanandvarianceareconstantacrosstime,andthecovariancejustdependsonthedistanceacrosstimeThreeNon-StationaryAR(1)TimeSeries-30-25-20-15

-10-50510152013579111315171921232527293133353739rho=1rho=1.25rho=-1.25ARandomWalkandARandomWalkWithDrift-

6-4-202468135791113151719212325272931333537394143454749RandomWalkRandomWalkWithDriftRandomWalks⚫Arandomwalki

sanAR(1)modelwhereρ1=1,meaningtheseriesisnotweaklydependent⚫Witharandomwalk,theexpectedvalueofytisalwaysy0–i

tdoesn’tdependont⚫Var(yt)=σet,soitincreaseswitht⚫WesayarandomwalkishighlypersistentsinceE(yt+h|yt)=ytforallh≥1Ra

ndomWalks(continued)⚫Arandomwalkisaspecialcaseofwhat’sknownasaunitrootprocess⚫Notethattrendingandpersistencearedifferentthings–a

seriescanbetrendingbutweaklydependent,oraseriescanbehighlypersistentwithoutanytrend⚫Arandomwalkwithdrift

isanexampleofahighlypersistentseriesthatistrendingRandomWalkwithDriftvs.TrendStationaryAR(1)-3-11357911135791113151719212325

272931333537394143454749RandomWalkWithDriftTrendStationaryAR(1)TrendingTimeSeries⚫Economictimeseriesoftenhaveatrend⚫Justbecause2

seriesaretrendingtogether,wecan’tassumethattherelationiscausal⚫Often,bothwillbetrendingbecauseofother

unobservedfactors⚫Evenifthosefactorsareunobserved,wecancontrolforthembydirectlycontrollingforthetrend⚫Atrendingseriesc

annotbestationary,sincethemeanischangingovertime⚫Atrendingseriescanbeweaklydependent⚫Ifaseriesisweaklydependentandissta

tionaryaboutitstrend,wewillcallitatrend-stationaryprocessDetrending⚫Addingalineartrendtermtoaregressionist

hesamethingasusing“detrended”seriesinaregression⚫Detrendingaseriesinvolvesregressingeachvariableinthemodelont⚫Theresidualsformthedetrendedseries⚫B

asically,thetrendhasbeenpartialledoutWhyForecastDemand?⚫Bothpublicandprivateenterprisesoperateunderconditionsofuncertainty.⚫Managementw

ishestolimitthisuncertaintybypredictingchangesincost,price,sales,andinterestrates.⚫Accurateforecastingcanhelpdevel

opstrategiestopromoteprofitabletrendsandtoavoidunprofitableones.⚫Aforecastisapredictionconcerningthefuture.Goodforecasting

willreduce,butnoteliminate,theuncertaintythatallmanagersfeel.HierarchyofForecasting⚫Theselectionofforecastingtechniquesdependsinpartonthelevelofec

onomicaggregationinvolved.Thehierarchyofforecastingis:⚫NationalEconomy(GDP,interestrates,inflation,etc.)sectorsoftheeco

nomy(durablegoods)industryforecasts(automobilemanufacturers)•firmforecasts(FordMotorCompany)ForecastingCriteriaThecho

iceofaparticularforecastingmethoddependsonseveralcriteria:⚫costsoftheforecastingmethodcomparedwithitsgains⚫complexity

oftherelationshipsamongvariables⚫timeperiodinvolved⚫accuracyneededinforecast⚫theleadtimebetweenreceivinginformationandthedecis

iontobemadeSignificanceofForecasting⚫Theaccuracyofaforecastingmodelismeasuredbyhowclosetheactualvariable,Y,endsuptotheforecastingvariable,Y.⚫Forecast

erroristhedifference.(Y-Y)⚫Modelsdifferinaccuracy,whichisoftenbasedonthesquarerootoftheaveragesquaredforecasterroroveraserie

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

silyalteredaseconomychanges⚫EarlySignals--cancatchchangesandanomaliesindata⚫Complex--hardtokeeptrackofinteractionsintheprimaryvariabl

es⚫LackofTestsforAccuracy--can’teasilytesttheaccuracyinpriorperiods.ADVANTAGESLIMITATIONSAdvantagesOrganizerelationshipsBehavioralre

lationshipsTestsofreliabilityQuantitativeForecastingandtheUseofModelsLimitationsEconomychangesDataminingofsameinformationOnlyacrudeapproximation

“Economicforecastingisreallytheartofidentifyingtensionsorimbalancesintheeconomicprocessandunderstandinginwhatmannertheywillberesol

ved.”-A.GreenspanIseeaTroubleaheadAlanGreenspan--ChairmanoftheBoardofGovernorsoftheFederalReserveQualit

ativeForecasting1.ComparativeStaticsShiftsinDemandShiftsinSupplyForecastChangesinPricesandQuantities⚫Su

pposeIncomeShiftsPriceRisesQuantityRisesquantityPsupplyD1D2AB2.ExpertOpinionTheaverageforecastfromseveralexpertsisaConsen

susForecast.MeanMedianModePercentilesQuartilesExample:ApartmentRentsGivenbelowisasampleofmonthlyrentvalues($)forone-bedro

omapartments.Thedataisasampleof70apartmentsinaparticularcity.Thedataarepresentedinascendingorder.425430430435435435435435440440440

440440445445445445445450450450450450450450460460460465465465470470472475475475480480480480485490490490500

500500500510510515525525525535549550570570575575580590600600600600615615Mean⚫Themeanofadatasetistheaverageofallthedatavalues.⚫Ifthed

ataarefromasample,themeanisdenotedby⚫Ifthedataarefromapopulation,themeanisdenotedbym(mu).xxni==xNiExample:A

partmentRents⚫Mean425430430435435435435435440440440440440445445445445445450450450450450450450460460460465465465470470472475475475

480480480480485490490490500500500500510510515525525525535549550570570575575580590600600600600615615xxni===343567049080,.M

edian⚫Themedianisthemeasureoflocationmostoftenreportedforannualincomeandpropertyvaluedata.⚫Afewextremelylargei

ncomesorpropertyvaluescaninflatethemean.Median⚫Themedianofadatasetisthevalueinthemiddlewhenthedataitemsarearrangedinascendingorder

.⚫Foranoddnumberofobservations,themedianisthemiddlevalue.⚫Foranevennumberofobservations,themedianistheaverageofthe

twomiddlevalues.Example:ApartmentRentsMedian=50thpercentilei=(p/100)n=(50/100)70=35.5Averagingthe35thand36thdatavalues:Median=

(475+475)/2=4754254304304354354354354354404404404404404454454454454454504504504504504504504604604604654654654704

70472475475475480480480480485490490490500500500500510510515525525525535549550570570575575580590600600600600615615

Mode⚫Themodeofadatasetisthevaluethatoccurswithgreatestfrequency.⚫Thegreatestfrequencycanoccurattwoormoredifferentvalues.⚫Ifthedatahaveexactlyt

womodes,thedataarebimodal.⚫Ifthedatahavemorethantwomodes,thedataaremultimodal.Example:ApartmentRents450occur

redmostfrequently(7times)Mode=4504254304304354354354354354404404404404404454454454454454504504504504504504504604

6046046546546547047047247547547548048048048048549049049050050050050051051051552552552553554955057057057557558059060060060060061

5615Percentiles⚫Apercentileprovidesinformationabouthowthedataarespreadovertheintervalfromthesmallestvaluetothelargestvalue.⚫Admission

testscoresforcollegesanduniversitiesarefrequentlyreportedintermsofpercentiles.PercentilesThepthperce

ntileofadatasetisavaluesuchthatatleastppercentoftheitemstakeonthisvalueorlessandatleast(100-p)percentoftheitemstakeonthisval

ueormore.Arrangethedatainascendingorder.Computeindexi,thepositionofthepthpercentile.i=(p/100)nIfiisnotaninteger,roundup.Thepthpercentileisthevalueint

heithposition.Ifiisaninteger,thepthpercentileistheaverageofthevaluesinpositionsiandi+1.Example:ApartmentRents⚫90thPercentilei=(p/100)n=(90/100)70=63A

veragingthe63rdand64thdatavalues:90thPercentile=(580+590)/2=585425430430435435435435435440440440440440445445445445445450450450450450450450460460

460465465465470470472475475475480480480480485490490490500500500500510510515525525525535549550570570575575580590600600600600615615Quar

tiles⚫Quartilesarespecificpercentiles⚫FirstQuartile=25thPercentile⚫SecondQuartile=50thPercentile=Median⚫

ThirdQuartile=75thPercentileExample:ApartmentRents⚫ThirdQuartileThirdquartile=75thpercentilei=(p/100)n=(75/100)70=52.5=53Thirdquarti

le=5254254304304354354354354354404404404404404454454454454454504504504504504504504604604604654654654704704724754754

75480480480480485490490490500500500500510510515525525525535549550570570575575580590600600600600615615EXAMPLES:•IBESandZacksInvestment--earning

sforecastsofstockanalysts•ConferenceBoard--macroeconomicpredictions•LivingstonSurveys--macroeconomicforecastsof50-60econom

ists•DelphiTechnique--panelofdiverseexperts.1.Writeoutforecasts2.Showthemtootherpanelists3.meettoarriveatconsensusNote:problems

ofexpenseandintransigenceDelphiapproachTheDelphimethodrecognizeshumanjudgmentaslegitimateandusefulinputsingeneratingforecasts.Singleexpertssometime

ssufferbiases;groupmeetingssufferfrom"followtheleader"tendenciesandreluctancetoabandonpreviouslystatedopinions(Gatewoo

dandGatewood,1983,Fowles,1978).InordertoovercometheseshortcomingsthebasicnotionoftheDelphimethod,theoreticalassumptionsandme

thodologicalproceduresdevelopedinthe1950sand1960sattheRANDCorporation.Forecastsaboutvariousaspectofthefutureareoftenderivedthrough

thecollationofexpertjudgment.⚫Fowles(1978)describesthefollowingtenstepsfortheDelphimethod:⚫Formationofateamtoundertakeandmo

nitoraDelphionagivensubject;⚫Selectionofoneormorepanelstoparticipateintheexercise.Customarily,thepaneli

stsareexpertsintheareatobeinvestigated;⚫DevelopmentofthefirstroundDelphiquestionnaire;⚫Testingthequestionnaireforproperwor

ding(e.g.,ambiguities,vagueness);⚫Transmissionofthefirstquestionnairestothepanelists;⚫Analysisofthefirstroundresp

onses;⚫Preparationofthesecondroundquestionnaires(andpossibletesting);⚫Transmissionofthesecondroundquestionnairestothepanelists;⚫Ana

lysisofthesecondroundresponses(Steps7to9arereiteratedaslongasdesiredornecessarytoachievestabilityintheresults);⚫Preparationofarepor

tbytheanalysisteamtopresenttheconclusionsoftheexercise.3.Surveys⚫Samplebias--telephone,magazine⚫Bia

sedquestions--advocacysurveys⚫Ambiguousquestions⚫RespondentsmaylieonquestionnairesNewProductshavenohis

toricaldata--Surveyscanassessinterestinnewideas.SurveyResearchCenterofU.ofMich.doesrepeatsurveysofhouseholdsonBigTicketitems(Aut

os)CommonSurveyProblemsDirectionofsalescanbeindicatedbyothervariables.TIMEIndexofCapitalGoodspeakPEAKMotorControlSales

4MonthsExample:IndexofCapitalGoodsisa“leadingindicator”Therearealsolaggingindicatorsandcoincidentindicators4.EconomicIndicator

s(BarometricForecasting)LEADINGINDICATORS*M2moneysupply(-10.9)S&P500stockprices(-6.9)Newhousingpermits(-10.1)Initialunemployment

claims(-7.3)Ordersforplantandequipment(-3.9)COINCIDENTINDICATORSNonagriculturalemployment(+.9)Indexofindustrialproduction(-.6)Personal

incomelesstransferpayment(-.6)LAGGINGINDICATORSPrimerate(+12.2)Durationofunemployment(+4.4)Timegiveninmonths

fromchangeQuestionsWhyarecontractsandordersforplantandequipmentappropriateleadingindicators?Whyistheindexofindustrialproduction

anappropriatecoincidentindicator?Whyistheprimerateanappropriatelaggingindicator?ExamplesofIndicatorsCompositeExample:Oneindicatorrises4%andanothe

rrises6%TheCompositeIndexisa5%increase.DiffusionExample:WallStreetWeekwithelevenanalysts,where4arenegativeaboutstocksand7arepositive:T

heDiffusionIndexis7/11,or63.3%.InterpretingandUsingIndices⚫compositeindex-weightedaverageindexofindividualindicatorsind

exinterpretedintermsof%changecompositeindexofleadingeconomicindicators:sustainedincreaseindicateseconomicgrowth⚫diffusion

index-measureoftheproportionofindividualtimeseriesthatincreasefordiffusionindexofleadingeconomicindicators,ifindex

>50%,improvedconditionsareexpectedWhatWentWrongWithSUVsatFordMotorCo?⚫ChryslerintroducedtheMinivaninthe1980’s⚫Fordexpandedit

scapacitytoproducetheExplorer,itspopularSUV⚫Explorer’spriceraisedin1995substantiallyatsametimeasChrysler’sJeepCherokee

andGMexpandeditsChevroletSUV⚫MustconsiderresponseofrivalsinpricingdecisionsQuantitativeForecasting⚫TimeSeriesLo

oksForPatternsOrderedbyTimeNoUnderlyingStructure⚫EconometricModelsExplainsrelationshipsSupply&DemandRegressionModelsLiketechnic

alsecurityanalysisLikefundamentalsecurityanalysisTimeSeriesExaminePatternsinthePastTIMEToXXXDependentVariable⚫TimeSe

riesisaquantitativeforecastingmethodUsespastdatatoprojectthefuturelooksforhighestACCURACYpossible⚫Accu

racy(MSE&MAD)MeanSquaredError&MeanAbsoluteDeviation⚫Ft+1=f(At,At-1,At-2,...)LetF=forecastandLetA=actualdataM

SE=t=1[Ft-At]2/NTheLOWERtheMSEorMAD,thegreatertheaccuracyMAD=t=1|(Ft-At)|/NMethodsofTimeSeriesAnalysisforEconomicForecasting

1.NaiveForecastFt+1=AtMethodbestwhenthereisnotrend,onlyrandomerrorGraphsofsalesovertimewithandwithouttrendsNOTrendTrend2.MovingAver

age⚫Asmoothingforecastmethodfordatathatjumpsaround⚫Bestwhenthereisnotrend⚫3-PeriodMovingAve.Ft+1=[At+At-1+At-2]/3*****ForecastLin

eTIMEDependentVariable3.ExponentialSmoothing⚫AhybridoftheNaiveandMovingAveragemethods⚫Ft+1=.•At+(1-)Ft⚫Aw

eightedaverageofpastactualandpastforecast.⚫Eachforecastisafunctionofallpastobservations⚫Canshowthatforecastisbasedongeometricallydec

liningweights.Ft+1=.•At+(1-)••At-1+(1-)2••At-1+…FindlowestMSEtopickthebestalpha.4.Linear&5.Semi-log⚫Usedwhent

rendhasaconstantAMOUNTofchangeAt=a+b•T,whereAtaretheactualobservationsandTisanumericaltimevariable⚫UsedwhentrendisaconstantPERCENTAGE

rateLogAt=a+b•T,wherebisthecontinuouslycompoundedgrowthrateLinearTrendRegressionSemi-logRegressionMoreonSemi-logFormaproof⚫Suppose:

Salest=Sales0(1+G)twhereGistheannualgrowthrate⚫Takethenaturallogofbothsides:LnSt=LnS0+t•Ln(1+G)butLn(1+G)=g,theequival

entcontinuouslycompoundedgrowthrateSO:LnSt=LnS0+t•gLnSt=a+g•tNumericalExamples:6observationsMTB>Printc1-c3.SalesTimeLn-sales100.014.6051

7109.824.69866121.634.80074133.744.89560146.254.98498164.365.10169Usingthissalesdata,estimatesalesinperiod7usingalinearand

asemi-logfunctionalformTheregressionequationisSales=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-ratiopConstant4.504160.00642701.3

50.000Time0.0981830.00164959.540.000s=0.006899R-sq=99.9%R-sq(adj)=99.9%ForecastedSales@Time=7⚫LinearModel⚫Sales=85.0+12.7Ti

me⚫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li

nearSalesTimeLn-sales100.014.60517109.824.69866121.634.80074133.744.89560146.254.98498164.365.10169179.07semi-log173.97linearWhichpredictiondoyoup

refer?Semi-logisexponential76.ProceduresforSeasonalAdjustments⚫TakeratiosofA/Fforpastyears.Findtheaverageratio.Adjus

tbythispercentageIfaverageratiois1.02,adjustforecastupward2%⚫UseDummyVariablesinaregression:D=1if4thquarter;0othe

rwise12-quartersofdataIIIIIIIVIIIIIIIVIIIIIIIVQuartersdesignatedwithromannumerals.DummyVariablesforSeas

onalAdjustments⚫LetD=1,if4thquarterand0otherwise⚫Runanewregression:At=a+b•T+c•Dthe“c”coefficientgivestheamountoftheadjustmentforthefourthquart

er.ItisanInterceptShifter.⚫EXAMPLE:Sales=300+10•T+18•D12Observations,1999-Ito2001-IV,Forecastallof200

2.Sales(2002-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impliesthattheInterceptis318,whenD=1impliesthattheslopeis7,whenD=1EconometricModels⚫Specifythe

variablesinthemodel⚫EstimatetheparameterssingleequationorperhapsseveralstagemethodsQd=a+b•P+c•I+d•Ps+e•Pc⚫Butforecastsrequirees

timatesforfutureprices,futureincome,etc.⚫Oftencombineeconometricmodelswithtimeseriesestimatesoftheindependentvariable.GarbageinGarba

geoutexample⚫Qd=400-.5•P+2•Y+.2•PsanticipatepricingthegoodatP=$20Incomeisgrowingovertime,theestimateis:LnYt=2

.4+.03•T,andnextperiodisT=17.ThepricesofsubstitutesarelikelytobeP=$18.⚫FindQd⚫Y=e2.910=18.357⚫HenceQd=430.31