管理经济学--生意和经济的预测(1)

BusinessandEconomicForecastingChapter5DemandForecastingisacriticalmanagerialactivitywhichcomesintwoforms:QualitativeForecastingGivestheExpectedDirectionQuantitativeForecastingGivesthepreciseAmount2.7654%2002South-WesternPublishingTime-SeriesCharacteristics:SecularTrendandCyclicalVariationinWomen’sClothingSalesTime-SeriesCharacteristics:SeasonalPatternandRandomFluctuationsMicrosoftCorp.SalesRevenue,1984–2001Figure6.2WhiteNoiseandMA(1)TimeSeries-1.5-1-0.500.511.5135791113151719212325272931333537394143454749WhiteNoiseMA(1)AMA(1)ProcessAmovingaverageprocessoforderone[MA(1)]canbecharacterizedasonewherext=et+a1et-1,t=1,2,…withetbeinganiidsequencewithmean0andvarianceThisisastationary,weaklydependentsequenceasvariables1periodapartarecorrelated,but2periodsaparttheyarenot2eThreeStationaryAR(1)TimeSeries-3.5-2.5-1.5-0.50.51.5135791113151719212325272931333537394143454749rho=.1rho=.5rho=.90AnAR(1)ProcessAnautoregressiveprocessoforderone[AR(1)]canbecharacterizedasonewhereyt=ρyt-1+et,t=1,2,…withetbeinganiidsequencewithmean0andvarianceσ2Forthisprocesstobeweaklydependent,itmustbethecasethat|ρ|1Corr(yt,yt+h)=Cov(yt,yt+h)/(σyσy)=ρ1hwhichbecomessmallashincreasesThreeStationaryAR(1)TimeSeries1-4-3-2-101234135791113151719212325272931333537394143454749rho=-.1rho=-.5rho=-.9StationaryStochasticProcessAstochasticprocessisstationaryifforeverycollectionoftimeindices1≤t1…tmthejointdistributionof(xt1,…,xtm)isthesameasthatof(xt1+h,…xtm+h)forh≥1Thus,stationarityimpliesthatthext’sareidenticallydistributedandthatthenatureofanycorrelationbetweenadjacenttermsisthesameacrossallperiodsCovarianceStationaryProcessAstochasticprocessiscovariancestationaryifE(xt)isconstant,Var(xt)isconstantandforanyt,h≥1,Cov(xt,xt+h)dependsonlyonhandnotontThus,thisweakerformofstationarityrequiresonlythatthemeanandvarianceareconstantacrosstime,andthecovariancejustdependsonthedistanceacrosstimeThreeNon-StationaryAR(1)TimeSeries-30-25-20-15-10-50510152013579111315171921232527293133353739rho=1rho=1.25rho=-1.25ARandomWalkandARandomWalkWithDrift-6-4-202468135791113151719212325272931333537394143454749RandomWalkRandomWalkWithDriftRandomWalksArandomwalkisanAR(1)modelwhereρ1=1,meaningtheseriesisnotweaklydependentWitharandomwalk,theexpectedvalueofytisalwaysy0–itdoesn’tdependontVar(yt)=σet,soitincreaseswithtWesayarandomwalkishighlypersistentsinceE(yt+h|yt)=ytforallh≥1RandomWalks(continued)Arandomwalkisaspecialcaseofwhat’sknownasaunitrootprocessNotethattrendingandpersistencearedifferentthings–aseriescanbetrendingbutweaklydependent,oraseriescanbehighlypersistentwithoutanytrendArandomwalkwithdriftisanexampleofahighlypersistentseriesthatistrendingRandomWalkwithDriftvs.TrendStationaryAR(1)-3-11357911135791113151719212325272931333537394143454749RandomWalkWithDriftTrendStationaryAR(1)TrendingTimeSeriesEconomictimeseriesoftenhaveatrendJustbecause2seriesaretrendingtogether,wecan’tassumethattherelationiscausalOften,bothwillbetrendingbecauseofotherunobservedfactorsEvenifthosefactorsareunobserved,wecancontrolforthembydirectlycontrollingforthetrendAtrendingseriescannotbestationary,sincethemeanischangingovertimeAtrendingseriescanbeweaklydependentIfaseriesisweaklydependentandisstationaryaboutitstrend,wewillcallitatrend-stationaryprocessDetrendingAddingalineartrendtermtoaregressionisthesamethingasusing“detrended”seriesinaregressionDetrendingaseriesinvolvesregressingeachvariableinthemodelontTheresidualsformthedetrendedseriesBasically,thetrendhasbeenpartialledoutWhyForecastDemand?Bothpublicandprivateenterprisesoperateunderconditionsofuncertainty.Managementwishestolimitthisuncertaintybypredictingchangesincost,price,sales,andinterestrates.Accurateforecastingcanhelpdevelopstrategiestopromoteprofitabletrendsandtoavoidunprofitableones.Aforecastisapredictionconcerningthefuture.Goodforecastingwillreduce,butnoteliminate,theuncertaintythatallmanagersfeel.HierarchyofForecastingTheselectionofforecastingtechniquesdependsinpartonthelevelofeconomicaggregationinvolved.Thehierarchyofforecastingis:NationalEconomy(GDP,interestrates,inflation,etc.)sectorsoftheeconomy(durablegoods)industryforecasts(automobilemanufacturers)•firmforecasts(FordMotorCompany)ForecastingCriteriaThechoiceofaparticularforecastingmethoddependsonseveralcriteria:costsoftheforecastingmethodcomparedwithitsgainscomplexityoftherelationshipsamongvariablestimeperiodinvolvedaccuracyneededinforecasttheleadtimebetweenreceivinginformationandthedecisiontobemadeSignificanceofForecastingTheaccuracyofaforecastingmodelismeasuredbyhowclosetheactualvariable,Y,endsuptotheforecastingvariable,Y.Forecasterroristhedifference.(Y-Y)Modelsdifferinaccuracy,whichisoftenbasedonthesquarerootoftheaveragesquaredforecasterroroveraseriesofNforecastsandactualfiguresCalledarootmeansquareerror,RMSE.RMSE={(Y-Y)2/N}^^^QualitativeForecastingFlexibility--easilyalteredaseconomychangesEarlySignals--cancatchchangesandanomaliesindataComplex--hardtokeeptrackofinteractionsintheprimaryvariablesLackofTestsforAccuracy--ca