Identifying Optimal Indicators and Lag Terms for Nowcasting Models

IdentifyingOptimalIndicatorsandLagTermsforNowcastingModels JingXieWP/23/45 IMFWorkingPapersdescriberesearchinprogressbytheauthor(s)andarepublishedtoelicitcommentsandtoencouragedebate. TheviewsexpressedinIMFWorkingPapersarethoseoftheauthor(s)anddonotnecessarilyrepresenttheviewsoftheIMF,itsExecutiveBoard,orIMFmanagement. 2023 MAR ©2023InternationalMonetaryFundWP/23/45 IMFWorkingPaper InstituteforCapacityDevelopment IdentifyingOptimalIndicatorsandLagTermsforNowcastingModelsPreparedbyJingXie AuthorizedfordistributionbyPaulCashin March2023 IMFWorkingPapersdescriberesearchinprogressbytheauthor(s)andarepublishedtoelicitcommentsandtoencouragedebate.TheviewsexpressedinIMFWorkingPapersarethoseoftheauthor(s)anddonotnecessarilyrepresenttheviewsoftheIMF,itsExecutiveBoard,orIMFmanagement. ABSTRACT:Manycentralbanksandgovernmentagenciesusenowcastingtechniquestoobtainpolicyrelevantinformationaboutthebusinesscycle.Existingnowcastingmethods,however,havetwocriticalshortcomingsforthispurpose.First,incontrasttomachine-learningmodels,theydonotprovidemuchifanyguidanceonselectingthebestexplantoryvariables(bothhigh-andlow-frequencyindicators)fromthe(typically)largersetofvariablesavailabletothenowcaster.Second,inadditiontotheselectionofexplanatoryvariables,theorderoftheautoregressionandmovingaveragetermstouseinthebaselinenowcastingregressionisoftensetarbitrarily.ThispaperproposesasimpleprocedurethatsimultaneouslyselectstheoptimalindicatorsandARIMA(p,q)termsforthebaselinenowcastingregression.TheproposedAS-ARIMAX(AdjustedStepwiseAutoregressiveMovingAveragemethodswithexogenousvariables)approachsignificantlyreducesout-of-samplerootmeansquareerrorfornowcastsofrealGDPofsixcountries,includingIndia,Argentina,Australia,SouthAfrica,theUnitedKingdom,andtheUnitedStates. JELClassificationNumbers: C32,C53,E37,E52,011 Keywords: Nowcasting;MixedFrequency;Forecasting;BusinessCycles Author’sE-MailAddress: jxie2@imf.org *Acknowledgements: IwouldliketothankMr.SamOuliarisforprovidinginstrumentalguidancethroughoutthisresearch,andamgratefultoMr.PaulCashin,Mr.FeiHan,Ms.IvySabuga,Mr.AlexanderBorodin,andInstituteforCapacityDevelopmentcolleaguesfortheirhelpfulcomments.IamalsogratefultoMs.ElisaManarinjaraforhersupportalongthepublicationprocedure. WORKINGPAPERS IdentifyingOptimalIndicatorsandLagTermsforNowcastingModels PreparedbyJingXie Contents Section1.Introduction3 Section2.AutomaticARIMASelectionProcedure4 Section3.AdjustedStepwiseARIMAXVariableSelectionProcedureandaSimpleExample6 Section4.BenchmarkModels10 Section5.NowcastingMethodology11 Section6.NowcastingIndianRealGDP12 Section7.EmpiricalResults14 Section8.OtherCountryExamples19 Section9.Conclusion19 AnnexI.AS-ARIMAXProcedureCharts20 AnnexII.CandidateIndicatorsandThreeMainAttributes22 AnnexIII.OtherCountryExamples24 Bibliography34 FIGURES Figure1RealisticForecastEvaluation:ThreeBenchmarkModels17 Figure2RealisticForecastEvaluation:BridgeandU-MIDASModels18 TABLES Table1:Pre-SelecteddatatoNowcastIndia’sRealGDP7 Table2AutomaticARIMAStepwiseVariableSelection-Steps1and2Result8 Table3AutomaticARIMAStepwiseVariableSelection-Step3Result8 Table4AutomaticARIMAStepwiseVariableSelection–SelectedBaselineModel9 Table5AutomaticARIMAStepwiseVariableSelection–AdjustedBaselineModel9 Table6SelectedBaselineModel14 Table7TestingforSerialCorrelation:QStatistics15 Table8TestingforNormality:Jarque-BeraTest15 Table9TestingforHeteroskedasticity:Breusch-Pagan-Godfreytest15 Table10ForecastEvaluationComparison:RMSE16 Table11ForecastEvaluationComparison:TheilU216 Table12ForecastEvaluationComparisonforOtherCountries:RMSE19 Section1.Introduction WhenmajoreconomicshockssuchastheCOVID-19pandemicortheglobalfinancialcrisisoccur,governmentstypicallyusecounter-cyclicalpoliciestosoftentheseverityofthenegativeshocktorealgrossdomesticproduct(GDP).Suchevidence-drivencounter-cyclepolicyrequirestimelyinformationonthestateoftheeconomyrelativetotrend.Unfortunately,therequireddataisoftenunavailablebecauseof:(a)theso-called“ragged-edge”problemarisingfrompublicationlagsor,moregenerally,missingdatapoints,especiallyinthecaseofrealGDP(Wallis,1986)and(b)themixed/incompatiblefrequencieswithwhichkeyeconomicindicatorsareavailable(Armesto,Engemann,&Owyan,2010). Manycentralbanksandgovernmentagenciesusenowcastingtechniques(e.g.,Bridge,Mixed-DataSamplingandDynamicFactorModel)toaddresstheseissues.ExamplesincludetheEuropeanCentralBank(Bańbura,etal.,2013),theCentralBankofMalta(EllulandRuisi,2022),andtheFederalReserveBankofAtlanta(Higgins,2014).Nowcasting—theartofforecasting“thehereandnow”—enablesreal-timeforecastingoflowerfrequencyvariables(suchasrealGDPandinflation)usingmoretimelyindicatorsthathavesimilarorhigherfrequencies.Standardnowcastingmodelstypicallyinvolvetwosteps:(a)forecastingthehighfrequencyindicatorsinthepreferredbaselinenowcastingregressiontoeliminatetheraggededgeproblem;and(b)convertingthehighfrequencyindicatorstothetargetfrequencyofthebaselineregression.Thewaythisconversionproceedsidentifiesthespecificnowcastingprocedureused(seeSection5). Acrit