英国国家经济和社会研究所-英国GDP月度预测的新证据 Box A New Evidence on Nowcasting Monthly UK GDP

NationalInstituteUKEconomicOutlook-Summer2025

BoxA:NewEvidenceonNowcastingMonthlyUKGDP

ByPaulaBejaranoCarbo,RoryMacqueenandEfthymiosXylangouras

TheOfficeforNationalStatistics(ONS)publishesamonthlyestimateofgrossdomesticproduct(GDP)atalagofaround40daysfromtheendofthemonth,reflectingthetimeittakestocollatedataoneconomicoutput.Atthesametime,policymakersandbusinesseshaveaninterestinknowinghowtheUKeconomyisperformingasquicklyaspossible,especiallyduringtimesofcrisis.Asaresult,nowcastingorforecastinginrealtimeGDPasaccuratelyaspossibleishighlyimportant.

Since2018,NIESRhasproduceditsmonthlyGDPtrackerontheONSGDPestimatereleasedate,commentingonthelatestdatapointandproducingabottom-upforecast(i.e.constructedbyaggregatingsectoralforecasts)ofeconomicoutputuptotheendofthenextquarter(Karaetal.,2018).InBejaranoCarboetal.(2025),wedevelopthisfurther,inlightofnewdataseriesavailablesincethepandemic,andtheincreasingdemandfortimelysectoralnowcasts.

ThisarticleprovidesanoverviewofthemethodologyandresultsinBejaranoCarboetal.(2025).Weusealargedatasetofpublic-andprivate-sectorvariables,includingnewlyavailablerealtimeindicators,asinputsto28nowcastingmodels.Eachofthesemodelsisestimatedfor20industrialsectorstogeneratesectoralGVAnowcasts,whicharethenaggregatedtoproduceanowcastforoverallGDP.Wethenapplyempiricalalgorithmstocombinethesectoralnowcasts,hopingtogeneratebetterGDPnowcastsbyputtingmoreweightonnowcastsfrommodelswhichhavebeenmoreaccuratepreviously.Byanalysinghowthedifferentmodelsandmodelcombinationalgorithmsperformoveroursampleof57monthscoveringbefore,duringandaftertheCovid-19shock,weprovidenewevidenceonnowcastingUKGDP.

Data

Ourforecastvariableofinterestisthemonth-on-monthgrowthrateofUKgrossvalueadded(GVA).Ournowcastisconstructedindirectlyfromthebottomup,bynowcastingmonth-on-monthgrowthratesforeachofthetwentyconstituentindustrialsectorsofGVA(e.g.agriculture,construction,manufacturing,wholesaleandretailtrade,etc.).Intwentyindependentnowcasts,therefore,thetargetvariableisthemonthlygrowthrateofactivityinthesectorinquestion.

Weproduceone-month-aheadpseudo-out-of-samplenowcastsmeaningthatforeachofour57testperiodmonthsfromJune2019toMarch2024,wegenerateaforecastfortheupcomingpublicationmonthbasedondatawhichwouldhavebeenavailableonemonthbeforefirstrelease.Forexample,thefirstestimateofJanuary2024GDPwaspublishedon14March2024;ourpseudoout-of-samplenowcastisconditionalondataavailableby13February2024(afterthefirstestimateofDecember2023GDPwaspublished).

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Thedatathatweconditionthesenowcastsonincludelaggedvaluesofthetargetvariablesaswellascontemporaneousandlaggedvaluesofawiderangeofexternalregressors.Thelatteraresourcedfrombothpublicandprivatesectorsources,andincludevariablesrelatedtobusinessandconsumerconfidence,prices,financialmarkets,trade,weather,labourmarkets,andCovid-specificindicators.

Models

Weestimateatotalof28statisticalmodels,describedindetailinBejaranoCarboetal.

(2025).

Foreachsector,weestimate:fourunivariatemodels,whichproducenowcastsbasedonlyonlaggedvaluesoftheforecastvariables;twolimited-informationmultivariatemodels,whichproducenowcastsbasedonlaggedvaluesoftheforecastvariablesandselectedexternalregressors,chosenbasedonourexperiencewiththeNIESRtrackerandinotherforecastingroles;andonefull-informationmodelmakinguseofourfulldataset(167variables).Foreachsector,eachofthesesevennowcastsismade,firstly,withouttreatmentofoutliersandthenwith,doublingthenumberofnowcaststo14.Wethenconsiderbothrecursiveestimation(inwhichallavailabledataisusedwhenestimatingmodelparameters)andarollingwindowestimationprocedure(inwhichonlythe36mostrecentmonthlyobservationsareused),doublingourtotalnumberofnowcastsgeneratedineachmonthforeachsectorto28.

Single-ModelResults

Weevaluatehowtheabove28modelsperformonceaggregatedacrossallsectorstoderiveasingle-modelGDPnowcast.

Fromthisexercise,wefindthatoutliertreatmentimprovesforecastaccuracy,asmeasuredbyRootMeanSquaredForecastError(RMSFE),significantlyduringtheCovidperiod(2020-2021)buthaslimitedeffectsinthepost-pandemicperiod(2022-2024).Amonguntreatedmodels,univariateapproachesperformpoorlyduringCovidcomparedtobigdataapproaches,butthesimplerunivariatemodelsareamongthebestinthepost-pandemicperiod.

Forecastperformancecanbeenhancedusingabottom-upapproachrelativetoatop-downapproachforasimpleunivariatemodel.Specifically,therecursivebottom-upARMA(1,1)withoutoutliertreatmentoutperformsorisequivalenttothebenchmarktop-downGVAARMA(1,1)inallsub-sampleperiods.

Thesameisnotalwaystrueforbigdataapproaches:atop-downDynamicLassowithPrincipalComponentAnalysis(PCA)beatsthebottom-upDynamicLassowithPCAoverallandinsub-samples.Infact,itisthebest-performingpurelystatisticalmodelwithoutoutliertreatmentduringtheCovid-19period.

Ultimately,noneofthesinglestatisticalmodelscanbeatthejudgment-augmentedNIESRnowcastsnortheONSfirstestimate,whenconsideredasforecastsofmaturedatavintages.

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NowcastCombinationAlgorithms

Thereisnoreasontobelievethatthedifferentsectorsoftheeconomyfollowthesamedata-generatingprocessandthereforearebestpredictedbythesamesingle-modelapproach.Therefore,afterusingthesamemodellingtechniqueforeachsector,weconsidermodelselectionapproacheswhichoptimallycombineforecastsforeachsector.ThisisinthespiritoftheNIESRGDPtrackerapproach,inthatdifferentfunctionalformsarepermittedbetweensectors.

Conceptually,thisrepresentsabottom-upforecastfortotalGDPgrowth,whichwouldhavebeenmadebyaforecasteronemonthbeforethisperiodsfirstestimateispublished,lookingatallthepasterrorsforeachofthemodelsforeachsector,andweightingnowcastsforeachsectorbasedonthemodel(s)estimatedtohavebeenleastinaccurateinthepast.

Firstly,aCumulativeRMSFESelectionalgorithmcalculatestheRMSFEofeachofthe28nowcastingmodelsforeachsectoruptoandincludingthemostrecentperiodandthenselectsthemodelforeachsectorwhichhasthesmallestcumulativeRMSFE.Informationfromtheothermodelnowcastsisdiscardedasalltheweightisputonthebestpreviouslyperformingmodelforeachsector.

Secondly,theDynamicModelAveragingRMSFE(DMA-RMSFE)algorithmcombinesnowcastsbyplacinggreaterweightonnowcastsfrommodelswithasmallerRMSFE.Thus,allinformationfromallmodelsreceivessomeweightinthiscase.

ThefinalalgorithmDynamicModelAveragingMAE(DMA-MAE),isnearlyidenticaltothesecond,butusesthemeanaverageerror(MAE)asitsweightingcriterionratherthantheRMSFE,astheformerismorerobusttooutliers.

Results:AggregateGDPNowcasting,2019-2024

FigureA1graphstheone-step-aheadnowcastsformonth-on-monthGDPgrowthfromthethreecombinationalgorithms.AsidefromtheinitialCovid-19shock,aclearoutlier,itappearsthatanydifferencebetweenthealgorithmicapproachesisminor,indicatingthattheirnowcastsanderrorsarehighlycorrelated.

Thatsaid,westillobservethattheCumulativeRMSFESelectionalgorithmunderperformsothers(intermsofRMSFE)duringtheinitialCovid-19shockbutmarginallyoutperformstheweightingalgorithmsin2022-2024.Perhapsunsurprisingly,thealgorithmwhichusesMAEperformsbestinthepandemicperiod,whenitisoptimaltobelesssensitivetooutlierforecasterrors.

3

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Percent

FigureA1One-stepaheadnowcastsformonthlyGDPgrowthJune2019-April2024(percent)

13

3

-7

ModelSelection-CumulativeRMSFE

ModelSelection-DMARMSFE

TableA1:

-17

ModelSelection-DMAMAE

Actual

-27

20192020202120222023

Source:Authors’calculations.

TablesA1-A3comparetheDMA-MAEalgorithmagainst3benchmarks–asimplerecursivetop-downARMA(1,1)model,theONSfirstestimateofGVA,andtheNIESRtrackerone-step-aheadforecast–andtheactualGDPdataoutturn.TableA1containsthiscomparisonforthewholesampleperiod,whiletablesA2andA3narrowresultsdowntotheCovidandpost-Covidsub-sampleperiods.

TableA1AccuracymetricsforGDPgrowthnowcasts2019-24

RMSFE

Bias

CumulativeRMSFE

DMARMSFE

DMAMAE

4.63

4.49

4.07

-0.34

-0.15

-0.06

InfeasibleBestModels

2.21

0.26

Top-downARMA

Top-downDynamicLassowithPCA

NIESRGDPTracker

FirstEstimate

6.78

4.81

1.57

0.64

-0.35

-0.04

0.11

-0.16

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TableA2AccuracymetricsforGDPgrowthnowcasts2020-21

RMSFE

Bias

CumulativeRMSFE

7.10

-0.77

DMARMSFE

6.88

-0.33

DMAMAE

6.24

-0.10

InfeasibleBestModels

3.40

0.58

10.42

7.37

2.38

0.95

-0.80

-0.06

0.25

-0.42

Top-downARMA

Top-downDynamicLassowithPCANIESRGDPTracker

FirstEstimate

TableA3AccuracymetricsforGDPgrowthnowcasts2022-24

RMSFE

Bias

CumulativeRMSFE

0.59

-0.06

DMARMSFE

0.64

-0.03

DMAMAE

0.63

-0.03

InfeasibleBestModels

0.26

0.04

0.66

0.73

0.38

0.20

-0.03

-0.03

-0.01

0.01

Top-downARMA

Top-downDynamicLassowithPCANIESRGDPTracker

FirstEstimate

Duringthepandemicperiod,thebestnowcastscomefromthejudgement-augmentedNIESRmodel,highlightingthechallengeofforecastingusingpurelystatisticalmodelsduringtimesofextremeandunprecedentedeconomicvolatility.Thatsaid,theNIESRnowcastperformssignificantlyworsethanthestatisticalmodelsduringthefourthquarterof2020

whentheUKgovernmentre-imposedstringentCovidrestrictionsduetothespreadofanewCovidvariantpossiblyreflectingoverly-pessimistichumanjudgementassociatedwithreceiving(andexperiencing)thisnews.

Duringthepandemicsub-sample,thealgorithmicDMA-MAEmodelimprovessignificantlyonthetop-downARMA(1,1)approach.Indeed,acrossthefullsampleof57months,aswellastheseparateCovidandpost-Covidsub-samples,allthreebottom-upalgorithmsoutperformthetop-downARMA(1,1)andtop-downDynamicLassowithPCAbenchmarks.Further,whilenoneofthealgorithmscancompetewiththeNIESRjudgement-augmentedforecastintermsofRMSFE,theDMA-MAEalgorithmgavelessbiasednowcastsduringtheinitialpandemicperiodthanboththeONSsfirstestimateandtheNIESRnowcasts.

Thoughthesingle-modelapproacheswithoutliertreatmentperformbetterthanthecombinationnowcastsduringtheCovidperiod,thecombinationalgorithmsaregenerallynoworsethanthesinglemodelsinnormaltimes.

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Finally,andpurelyasarobustnesscheck,wecreateaseriesofnowcastsobtainedbyselectingthebestnowcastforeachsectorexpostandcallthisinfeasiblealgorithmastheBestModelsalgorithm.Thisclearlyimplausiblecomparatorenablesustoseehowwellourapproachwoulddoifwewereabletoalwayschoosethemostaccurateforecast.WefindthattheBestModelsalgorithmdoesfarbetterthanthecombinationalgorithms,suggestingthatchoosingthebestnowcastmaybeatleastasimportantasgeneratingmoreorbetternowcastsopeninganotherinterestingavenueforfurtherresearch.

Results:SectoralGDPNowcasting,2019-2024

TableA4displaystheRMSFEandbias(averageerror)oftheDMA-MAEalgorithmforeachsector,whichhelpsunderstandthesectoralsourceofnowcasterrorsinthismodel.Thetablealsodisplaysthestandarddeviationofthetargetseries,aswellastheRMSFEdividedbythestandarddeviationtorepresentthesizeoftheforecasterrorsrelativetothevolatilityoftheseries.Thishelpsustoseewhetherlarge(small)forecasterrorscanbeattributedtothehigh(low)volatilityofthesectorgrowthseriesorotherfactors.ThetablealsocontainstheRMSFEoftheONSfirstestimateofsectoralGVA.Thetableindicatesthatinsomecases(highlightedinbold)themodelnowcastsaremoreaccurateintermsofRMSFEthantheONSsfirstestimate.

PolicyRecommendations

Pendingfurtherresearchalongthelinesweproposeabove,wewouldsummariseouradvicetotheeconomistnowcastingmonthlygrowthratesforthisquarterandthenextasfollows:

1.Useabottom-upapproach

2.Usesimpletime-seriesmodelsoraforecastcombinationapproachtoforecasteachofthebottomupelements

3.EmployaK-Nearest-Neighbourorsimilaralgorithmtotreatoutliersinthedata

4.Applyjudgementwhenyoucanseeashockthatthemodelcannot

5.Considerawiderrangeofinputvariablesandbig-datatop-downnowcastingmethodsinthepresenceofgreate