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BusinessandEconomicForecastingChapter5DemandForecastingisacriticalmanagerialactivitywhichcomesintwoforms:QualitativeFore

castingGivestheExpectedDirectionQuantitativeForecastingGivesthepreciseAmount2.7654%©2002South-WesternPubli

shingTime-SeriesCharacteristics:SecularTrendandCyclicalVariationinWomen’sClothingSalesTime-SeriesCharacteristics:SeasonalPatternan

dRandomFluctuationsMicrosoftCorp.SalesRevenue,1984–2001Figure6.2WhiteNoiseandMA(1)TimeSeries-1.5-1-0.500.511.51357911131517192123252729313335

37394143454749WhiteNoiseMA(1)AMA(1)Process⚫Amovingaverageprocessoforderone[MA(1)]canbecharacterizedasonewherext=et+a1et-1,t

=1,2,…withetbeinganiidsequencewithmean0andvariance⚫Thisisastationary,weaklydependentsequenceasvariables1periodapartareco

rrelated,but2periodsaparttheyarenot2eThreeStationaryAR(1)TimeSeries-3.5-2.5-1.5-0.50.51.5135791113151719212325272

931333537394143454749rho=.1rho=.5rho=.90AnAR(1)Process⚫Anautoregressiveprocessoforderone[AR(1)]canbecharac

terizedasonewhereyt=ρyt-1+et,t=1,2,…withetbeinganiidsequencewithmean0andvarianceσ2Forthisprocesstobeweaklydependent,itm

ustbethecasethat|ρ|<1⚫Corr(yt,yt+h)=Cov(yt,yt+h)/(σyσy)=ρ1hwhichbecomessmallashincreasesThreeStationar

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

ticProcess⚫Astochasticprocessisstationaryifforeverycollectionoftimeindices1≤t1<…<tmthejointdistributionof

(xt1,…,xtm)isthesameasthatof(xt1+h,…xtm+h)forh≥1⚫Thus,stationarityimpliesthatthext’sareidenticallydistributedandthatthenatureofanycorre

lationbetweenadjacenttermsisthesameacrossallperiodsCovarianceStationaryProcess⚫AstochasticprocessiscovariancestationaryifE(xt)isconstant,Var(xt)isc

onstantandforanyt,h≥1,Cov(xt,xt+h)dependsonlyonhandnotont⚫Thus,thisweakerformofstationarityrequiresonlythatthemeanandvari

anceareconstantacrosstime,andthecovariancejustdependsonthedistanceacrosstimeThreeNon-StationaryAR(1)TimeSeries-30-25-20-15-10-5051015

2013579111315171921232527293133353739rho=1rho=1.25rho=-1.25ARandomWalkandARandomWalkWithDrift-6-4-20246813579111315171921232527293133353739414345474

9RandomWalkRandomWalkWithDriftRandomWalks⚫ArandomwalkisanAR(1)modelwhereρ1=1,meaningtheseriesisnotweaklydependent⚫Witharandomwalk,thee

xpectedvalueofytisalwaysy0–itdoesn’tdependont⚫Var(yt)=σet,soitincreaseswitht⚫WesayarandomwalkishighlypersistentsinceE(yt+h

|yt)=ytforallh≥1RandomWalks(continued)⚫Arandomwalkisaspecialcaseofwhat’sknownasaunitrootprocess⚫Notethattrendingandpersistencearediff

erentthings–aseriescanbetrendingbutweaklydependent,oraseriescanbehighlypersistentwithoutanytrend⚫Arandomwalkwithdriftisanexampleofahighlypersis

tentseriesthatistrendingRandomWalkwithDriftvs.TrendStationaryAR(1)-3-11357911135791113151719212325272931333537394143454749RandomWalkWith

DriftTrendStationaryAR(1)TrendingTimeSeries⚫Economictimeseriesoftenhaveatrend⚫Justbecause2seriesaretrendingtog

ether,wecan’tassumethattherelationiscausal⚫Often,bothwillbetrendingbecauseofotherunobservedfactors⚫Evenifthosefactorsareunobs

erved,wecancontrolforthembydirectlycontrollingforthetrend⚫Atrendingseriescannotbestationary,sincethemeanischangingov

ertime⚫Atrendingseriescanbeweaklydependent⚫Ifaseriesisweaklydependentandisstationaryaboutitstrend,wewillcallitatrend-stationaryprocessDetr

ending⚫Addingalineartrendtermtoaregressionisthesamethingasusing“detrended”seriesinaregression⚫Detrendingaseries

involvesregressingeachvariableinthemodelont⚫Theresidualsformthedetrendedseries⚫Basically,thetrendhasbeenpartialledoutWhyForecastDemand?⚫Bothpublican

dprivateenterprisesoperateunderconditionsofuncertainty.⚫Managementwishestolimitthisuncertaintybypredictingchangesincost,price,

sales,andinterestrates.⚫Accurateforecastingcanhelpdevelopstrategiestopromoteprofitabletrendsandtoavoidunprofitableones.⚫Aforecastisapredictionco

ncerningthefuture.Goodforecastingwillreduce,butnoteliminate,theuncertaintythatallmanagersfeel.HierarchyofForecastin

g⚫Theselectionofforecastingtechniquesdependsinpartonthelevelofeconomicaggregationinvolved.Thehierarchyofforecastingis:⚫NationalEconomy(GDP,interest

rates,inflation,etc.)sectorsoftheeconomy(durablegoods)industryforecasts(automobilemanufacturers)•firmforecasts(FordMotorCompany)ForecastingCri

teriaThechoiceofaparticularforecastingmethoddependsonseveralcriteria:⚫costsoftheforecastingmethodcomparedwithitsgains⚫c

omplexityoftherelationshipsamongvariables⚫timeperiodinvolved⚫accuracyneededinforecast⚫theleadtimebetween

receivinginformationandthedecisiontobemadeSignificanceofForecasting⚫Theaccuracyofaforecastingmodelismeasuredbyh

owclosetheactualvariable,Y,endsuptotheforecastingvariable,Y.⚫Forecasterroristhedifference.(Y-Y)⚫Modelsdifferinaccuracy,whichisofte

nbasedonthesquarerootoftheaveragesquaredforecasterroroveraseriesofNforecastsandactualfigures⚫Calledarootmeansquareerror,RMSE.RMSE={(Y-Y)2/N}^^^

QualitativeForecasting⚫Flexibility--easilyalteredaseconomychanges⚫EarlySignals--cancatchchangesandanomaliesindata⚫Complex--har

dtokeeptrackofinteractionsintheprimaryvariables⚫LackofTestsforAccuracy--can’teasilytesttheaccuracyinpriorperiods.ADVANTAGESLIMITATIONSAdvantagesOr

ganizerelationshipsBehavioralrelationshipsTestsofreliabilityQuantitativeForecastingandtheUseofModelsLimitationsEconomychangesDataminingo

fsameinformationOnlyacrudeapproximation“Economicforecastingisreallytheartofidentifyingtensionsorimbalancesintheeconomicproce

ssandunderstandinginwhatmannertheywillberesolved.”-A.GreenspanIseeaTroubleaheadAlanGreenspan--ChairmanoftheBoardofGov

ernorsoftheFederalReserveQualitativeForecasting1.ComparativeStaticsShiftsinDemandShiftsinSupplyForecastChangesinPricesandQuantities⚫Suppos

eIncomeShiftsPriceRisesQuantityRisesquantityPsupplyD1D2AB2.ExpertOpinionTheaverageforecastfromseveralexpertsisaConsensusForecast.Mean

MedianModePercentilesQuartilesExample:ApartmentRentsGivenbelowisasampleofmonthlyrentvalues($)forone-bedroomapartments.Thed

ataisasampleof70apartmentsinaparticularcity.Thedataarepresentedinascendingorder.425430430435435435435435440440440440440445

4454454454454504504504504504504504604604604654654654704704724754754754804804804804854904904905005005005005105105155255255255355495505

70570575575580590600600600600615615Mean⚫Themeanofadatasetistheaverageofallthedatavalues.⚫Ifthedataarefromasample,themeanisdenotedby⚫

Ifthedataarefromapopulation,themeanisdenotedbym(mu).xxni==xNiExample:ApartmentRents⚫Mean425430430435435435435435440440440440440445445445445445

4504504504504504504504604604604654654654704704724754754754804804804804854904904905005005005005105105155255255255355495505705705755755805

90600600600600615615xxni===343567049080,.Median⚫Themedianisthemeasureoflocationmostoftenreportedforannualincome

andpropertyvaluedata.⚫Afewextremelylargeincomesorpropertyvaluescaninflatethemean.Median⚫Themedianofadatasetisthevalueinthemiddlewhenthedataitemsa

rearrangedinascendingorder.⚫Foranoddnumberofobservations,themedianisthemiddlevalue.⚫Foranevennumberof

observations,themedianistheaverageofthetwomiddlevalues.Example:ApartmentRentsMedian=50thpercentilei=(p/100)n=(50/100)70=35.5Averagingthe3

5thand36thdatavalues:Median=(475+475)/2=475425430430435435435435435440440440440440445445445445445450450450450450450

450460460460465465465470470472475475475480480480480485490490490500500500500510510515525525525535549550

570570575575580590600600600600615615Mode⚫Themodeofadatasetisthevaluethatoccurswithgreatestfrequency.⚫Thegreatestfrequencyc

anoccurattwoormoredifferentvalues.⚫Ifthedatahaveexactlytwomodes,thedataarebimodal.⚫Ifthedatahavemorethantwomodes,thedataaremultimodal.Example:

ApartmentRents450occurredmostfrequently(7times)Mode=45042543043043543543543543544044044044044044544544544544545045045045045045045046046

0460465465465470470472475475475480480480480485490490490500500500500510510515525525525535549550570570575575580590600600600600615615Percentiles⚫Ap

ercentileprovidesinformationabouthowthedataarespreadovertheintervalfromthesmallestvaluetothelargestvalue.⚫Admissiontestscoresforcollegesandun

iversitiesarefrequentlyreportedintermsofpercentiles.PercentilesThepthpercentileofadatasetisavaluesuchthatatleastppercentoftheitemsta

keonthisvalueorlessandatleast(100-p)percentoftheitemstakeonthisvalueormore.Arrangethedatainascendingorder.Computeindexi,thepositionofthepthper

centile.i=(p/100)nIfiisnotaninteger,roundup.Thepthpercentileisthevalueintheithposition.Ifiisaninteger,thepthpercentileistheaverageofthevalues

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

/2=5854254304304354354354354354404404404404404454454454454454504504504504504504504604604604654654654704704724754754754804804804804854904904905005

00500500510510515525525525535549550570570575575580590600600600600615615Quartiles⚫Quartilesarespecificpe

rcentiles⚫FirstQuartile=25thPercentile⚫SecondQuartile=50thPercentile=Median⚫ThirdQuartile=75thPercentileExa

mple:ApartmentRents⚫ThirdQuartileThirdquartile=75thpercentilei=(p/100)n=(75/100)70=52.5=53Thirdquartile=5254254304304354354354354354404404

4044044044544544544544545045045045045045045046046046046546546547047047247547547548048048048048549049049050050050050051051051552552552553554955057057

0575575580590600600600600615615EXAMPLES:•IBESandZacksInvestment--earningsforecastsofstockanalysts•ConferenceBoard--macroeconomicpredictions•Li

vingstonSurveys--macroeconomicforecastsof50-60economists•DelphiTechnique--panelofdiverseexperts.1.Writeout

forecasts2.Showthemtootherpanelists3.meettoarriveatconsensusNote:problemsofexpenseandintransigenceDelphiapproachTheDelphimethodrecognizeshumanjud

gmentaslegitimateandusefulinputsingeneratingforecasts.Singleexpertssometimessufferbiases;groupmeetingssufferfrom"followtheleader"tendenci

esandreluctancetoabandonpreviouslystatedopinions(GatewoodandGatewood,1983,Fowles,1978).Inordertoovercometheseshortcomingsthebasicnotio

noftheDelphimethod,theoreticalassumptionsandmethodologicalproceduresdevelopedinthe1950sand1960sattheRANDCorporation.Forecastsa

boutvariousaspectofthefutureareoftenderivedthroughthecollationofexpertjudgment.⚫Fowles(1978)describesthefollowingtenstepsf

ortheDelphimethod:⚫FormationofateamtoundertakeandmonitoraDelphionagivensubject;⚫Selectionofoneormorepa

nelstoparticipateintheexercise.Customarily,thepanelistsareexpertsintheareatobeinvestigated;⚫DevelopmentofthefirstroundDelphiquestionnaire;⚫Te

stingthequestionnaireforproperwording(e.g.,ambiguities,vagueness);⚫Transmissionofthefirstquestionnairestothepanelists;⚫Analysisoft

hefirstroundresponses;⚫Preparationofthesecondroundquestionnaires(andpossibletesting);⚫Transmissionofthese

condroundquestionnairestothepanelists;⚫Analysisofthesecondroundresponses(Steps7to9arereiteratedaslongasdesiredornece

ssarytoachievestabilityintheresults);⚫Preparationofareportbytheanalysisteamtopresenttheconclusionsoftheexercise

.3.Surveys⚫Samplebias--telephone,magazine⚫Biasedquestions--advocacysurveys⚫Ambiguousquestions⚫Respondentsmaylieonq

uestionnairesNewProductshavenohistoricaldata--Surveyscanassessinterestinnewideas.SurveyResearchCenterofU.ofMich.doesrepeatsurveysofho

useholdsonBigTicketitems(Autos)CommonSurveyProblemsDirectionofsalescanbeindicatedbyothervariables.TIMEIndexofCapita

lGoodspeakPEAKMotorControlSales4MonthsExample:IndexofCapitalGoodsisa“leadingindicator”Therearealsolaggingindicatorsandcoincidentindicators4.Economic

Indicators(BarometricForecasting)LEADINGINDICATORS*M2moneysupply(-10.9)S&P500stockprices(-6.9)Newhousing

permits(-10.1)Initialunemploymentclaims(-7.3)Ordersforplantandequipment(-3.9)COINCIDENTINDICATORSNonagriculturalemployment(

+.9)Indexofindustrialproduction(-.6)Personalincomelesstransferpayment(-.6)LAGGINGINDICATORSPrimer

ate(+12.2)Durationofunemployment(+4.4)TimegiveninmonthsfromchangeQuestionsWhyarecontractsandordersforplantandequipmentappropriateleadin

gindicators?Whyistheindexofindustrialproductionanappropriatecoincidentindicator?Whyistheprimerateanappropriatelaggingindicator?Exa

mplesofIndicatorsCompositeExample:Oneindicatorrises4%andanotherrises6%TheCompositeIndexisa5%increase.DiffusionExample:Wa

llStreetWeekwithelevenanalysts,where4arenegativeaboutstocksand7arepositive:TheDiffusionIndexis7/11,or63.3%.InterpretingandUsingIndices⚫co

mpositeindex-weightedaverageindexofindividualindicatorsindexinterpretedintermsof%changecompositeindexofleadingeconomicindica

tors:sustainedincreaseindicateseconomicgrowth⚫diffusionindex-measureoftheproportionofindividualtimeseriesthatincre

asefordiffusionindexofleadingeconomicindicators,ifindex>50%,improvedconditionsareexpectedWhatWentWr

ongWithSUVsatFordMotorCo?⚫ChryslerintroducedtheMinivaninthe1980’s⚫FordexpandeditscapacitytoproducetheExplorer,itspopularSUV⚫Explorer’spricera

isedin1995substantiallyatsametimeasChrysler’sJeepCherokeeandGMexpandeditsChevroletSUV⚫Mustconsiderresponseofrivalsinpricingd

ecisionsQuantitativeForecasting⚫TimeSeriesLooksForPatternsOrderedbyTimeNoUnderlyingStructure⚫Econometr

icModelsExplainsrelationshipsSupply&DemandRegressionModelsLiketechnicalsecurityanalysisLikefundamentalsecurityanalysisTimeSeriesExamineP

atternsinthePastTIMEToXXXDependentVariable⚫TimeSeriesisaquantitativeforecastingmethodUsespastdatatopr

ojectthefuturelooksforhighestACCURACYpossible⚫Accuracy(MSE&MAD)MeanSquaredError&MeanAbsoluteDeviation⚫Ft+1=f(At,At-1,At-2,

...)LetF=forecastandLetA=actualdataMSE=t=1[Ft-At]2/NTheLOWERtheMSEorMAD,thegreatertheaccuracyMAD=t=1|(Ft-A

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

rtimewithandwithouttrendsNOTrendTrend2.MovingAverage⚫Asmoothingforecastmethodfordatathatjumpsaround⚫Bestwhenthereisnotrend⚫3-PeriodMovingAve.

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

ods⚫Ft+1=.•At+(1-)Ft⚫Aweightedaverageofpastactualandpastforecast.⚫Eachforecastisafunctionofallpastobservations⚫Canshowthatforecastisbasedongeom

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

ofchangeAt=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,theequivalentcontinuouslycompoundedgrowthrateSO:LnS

t=LnS0+t•gLnSt=a+g•tNumericalExamples:6observationsMTB>Printc1-c3.SalesTimeLn-sales100.014.60517109.824.69866121.634.80074133.744.89560146.2

54.98498164.365.10169Usingthissalesdata,estimatesalesinperiod7usingalinearandasemi-logfunctionalformTheregressionequationisSales=85.0+12.7TimePredi

ctorCoefStdevt-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-ratiopConstant4.504160.00642701.350.000Time0.09818

30.00164959.540.000s=0.006899R-sq=99.9%R-sq(adj)=99.9%ForecastedSales@Time=7⚫LinearModel⚫Sales=85.0+12.7

Time⚫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-sales100.014.60517109.824.69866121.634.80074133.744.89560146.254.98498164.365.1

0169179.07semi-log173.97linearWhichpredictiondoyouprefer?Semi-logisexponential76.ProceduresforSeasonalAdjustments⚫TakeratiosofA/Fforpastyears.Find

theaverageratio.AdjustbythispercentageIfaverageratiois1.02,adjustforecastupward2%⚫UseDummyVariablesinaregre

ssion:D=1if4thquarter;0otherwise12-quartersofdataIIIIIIIVIIIIIIIVIIIIIIIVQuartersdesignatedwithromannumerals.Dumm

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

ntforthefourthquarter.ItisanInterceptShifter.⚫EXAMPLE:Sales=300+10•T+18•D12Observations,1999-Ito2001-IV,Forecastallof2002.Sales(2002-I)=4

30;Sales(2002-II)=440;Sales(2002-III)=450;Sales(2002-IV)=478DummyVariableInteractions⚫Canintroduceaslopeshifterby“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impliesthattheslope

is7,whenD=1EconometricModels⚫Specifythevariablesinthemodel⚫EstimatetheparameterssingleequationorperhapsseveralstagemethodsQd=a+b•P+c•I+d•P

s+e•Pc⚫Butforecastsrequireestimatesforfutureprices,futureincome,etc.⚫Oftencombineeconometricmodelswithtimeseriesestimatesoftheind

ependentvariable.GarbageinGarbageoutexample⚫Qd=400-.5•P+2•Y+.2•PsanticipatepricingthegoodatP=$20Incomeisgrowingovertime,theestimate

is:LnYt=2.4+.03•T,andnextperiodisT=17.ThepricesofsubstitutesarelikelytobeP=$18.⚫FindQd⚫Y=e2.910=18.357⚫HenceQd=430.31