Post on 05-May-2020
"WHY COMBINING WORKS?"
by
Spyros MAKRIDAKIS*
N° 89 / 53
Research Professor of Decision Sciences and InformationSystems, INSEAD, Boulevard de Constance, 77305, Fontainebleau,France.
Director of Publication:
Charles WYPLOSZ, Associate Deanfor Research and Development
Printed at INSEAD,Fontainebleau, France.
WEY COMBINING %?ORKS?
Spyros MAKRIDAKIS
Research Professor, INSEAD
FORTHCOMING: INTERNATIONAL JOURNAL OF FORECASTING
Address
July 1989
INSEAD
Bld de Constance
77305 Fontainebleau
France
ktiY COMIUNING WO"r.KS?
Spyros MAKRIDAKIS
Research Professor, INSEAD
Abstract
The purpose of this paper is to explore the reasons why combining
works, discuss the implications involved and propose guidelines for improving
the field of forecasting by exploiting the reasons that contribute to the
success of combining.
Keywords: Time Series Forecasting; Forecasting Accuracy; Combining
There is little doubt that combining improves forecasting accuracy.
This empirical finding holds true in statistical forecasting, judgmental
estimates and when averaging statistical and subjective predictions (Clemen,
1989). In addition, combining reduces the variance of post-sample forecasting
errors considerably (Makridakis and Winkler, 1983). The empirical findings
are at odds with statistical theory and point out the need for major changes
in our basic thinking and approach to statistical modelling and forecasting.
As Clemen (1989) concludes "using a combination of forecasts amounts to an
admission that the forecaster is unable to build a properly specified model.
Trying ever more elaborate combining models seems to add insult to injury as
the more complicated combinations do not generally perform all that well."
FACTORS TLIAT CONTRIBUTE TO MAKING COMBINING WORK
There are several factors that deteriorate the accuracy of
individual forecasting methods and increase the size of errors. Combining
works because it averages such errors. The following factors are a partial
list that contribute to the empirical fact that the accuracy of combining is
higher chan those of the individual methods being combined:
1. Measuring the wrong thing: In forecasting we often need to estimate
damand however damand data is rarely, if ever, available. Thus, instead of
measuring demand we measure such things as orders, production, shipments or
billings. However it is obvious that such proxies of apparent demand
introduce systematic biases in measuring the "real" demand and therefore
decrease accuracy of forecasting.
2. Measurement Errors: No matter what we try to measure there are always
errors of measurement (including clerical and data processing errors) the size
of which can be substantial and systematic. This is particularly true for
disaggregate items but can be also observed on aggregate ones (e.g., GNP - see
Morgenstern, 1963) whose magnitude range from plus of minus 10% to 159.
Measurement errors also include accounting changes, the way the data is kept,
changes in definitions, and what is to be included in the different factors
being used. Even if the size of measurement errors is in the neighborhood of
10%-15% (which is a minimum that applies to highly aggregate macroeconomic
variables) it makes little sense to worry about better methods which are going
to improve forecasting accuracy 5% or 10%.
3. Unstable or changing patterns or relationships: Statistical models assume
that patterns and relationships are constant. However, this is rarely the
case in the real world where special events and actions, fashions, cycles and
so forth bring systematic changes and therefore introduce non-random errors in
forecasting.
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tuai past errors: Availaule forecasting methods select
the best model by a process that depends on how well a model minimizes one-
step-ahead forecasting errors when tested against available data. However,
such models are not necessarily unbiased in predicting future values (in
particular when there are changes in patterns or relationship) and in
forecasting more than one-step-ahead horizons.
CAN COMBINING BE IMPROVED?
Empirical evidence indicates that simple combining schemes (i.e„
using a simple arithmetic average to combine several/many methods) are as
accurate as elaborate ones. The following three factors have been found by
this author to improve the accuracy of combining while maintaining the idea of
using simple combining procedures:
1. Use sensible methods: Various forecasting methods can be checked
empirically concerning their individual ability to accurately forecast.
Alternatively, the findings of major empirical studies can be used to exclude
methods which are consistently worse than others. Once empirical evidence has
indicated a number of models which provide the most accurate results,
combining can subsequently be restricted to these set methods only, thus
excluding some which are clearly inferior (e.g., quadratic exponential
smoothing for longer forecasting horizons).
2. Use complementary methods: Some methods are conservative in forecasting
(for example, single exponential smoothing) while some others are over-
reactive and/or extrapolate past trend in a way that assumes that such trends
will continue uninterrupted during the future. By selecting methods which can
cover a vide range of possibilities the user can combine methods which cover a
wide range of outcomes and which when averaged can also average the
forecasting errors of the methods being combined.
3. Use combining to elicit judgemental inputs: Instead of making judgemental
estimates of future values this author has found it useful to ask decision
makers to indicate the direction of future changes in trends. If the
-3-
subjective judgment of those is that the trend is going to slow down
or become flat, then more weight can Ue given to a method like single
exponential smoothing. Alternatively .f decision makers feel that established
trends will continue, then more weight man be given to linear smoothing. If
the users are not certain the dampen trez.d model can be weighted more heavily.
Thus, by the appropriate selection of forecasting methods to include in the
combining (in particular if they are complementary) . and by deciding on the
appropriate weight of each (or alternatively which methods to combine) a way
can be found to elicit the judgment and knowledge of decision makers while
still harnessing the advantage of using objective and consistent approaches to
forecasting.
COMBINING AND FORECASTING RESEARCH
In addition to more appropriate data geared towards forecasting
applications the methods used to forecast must be also reconsidered. Methods
that fit the past, extrapolate past patterns/relationships and are concerned
with one-step-ahead forecasts are clearly not appropriate. Thus, a serious
effort must develop towards new, creative alternatives that are not based on
the fallacies of constancy of past patterns/relationships which has been the
hidden but prevalent assumption of all statistical forecasting. Some initial
attempts by this author (Makridakis 1990) to go beyond model fitting, and
select methods based on their performance on more than one-step-ahead
forecasts have produced encouraging results. Much more, however, must be done
if forecasting is to become useful and relevant for actual, real-life
applications.
The fact that the accuracy of combining outperforms the individual
methods and/or subjective estimates being combined cannot be ignored and must
be used to guide our search for improving forecasting accuracy. Effort must
be concentrated on gathering the right data and minimizing measurement errors.
Moreover, data must be adjusted to variations that are external to the
generating process (e.g., a strike of some other highly unusual event).
-4-
C()!.;CLUSIONS
Decision makers will benefit by accepting the empirical finding that
combining improves accuracy and reduces the variance of forecasting errors.
Similarly, forecasting researchers ought to test any new methods against a
combination of existing ones. Unless their new method is proven to outperform
the combination it should not be viewed favorably. Finally, forecasting
experts must accept the limitations of available forecasting methods and those
of the data being used and develop alternative approaches to forecasting which
are more realistic and relevant to actual forecasting situations.
-5-
References
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86/27 Karel COOLand Ingemar DIERICKA
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86/01
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86/02 Philippe A. NAERTMarcel VEVERBERGBand Cuido VERSVIJVEL
86/03 Nichael BRIMM
86/04 Spyros NAKRIDAXISand Michèle OISON
86/05 Charles A. VTPLOS2
86/06 Frencesco CIAVAllI,Joit R. SBEEN andCharles A. VTPLOSZ
86/07 Douglas L. KacLACHLANand Spyros MAKRIDAKIS
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86/34 Philippe RASPESLACHand David JEMISON
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86/36 Albert CORRAY andGabriel BAVAVINI
86/37 David GAUTSCRI andRoger BETANCOURT
86/38 Gabriel BAVAVINI
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87/09 Lister VICKERT,Mark PILKINCTONand Paul READ
87/10 André LAURENT
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87/12 Fernando BAATOLOMEand André LAURENT
87/13 Sumantra GHOSHALand Nitin NOIIRIA
87/14 Landis CABEL
87/15 Spyros HAKRIDAKIS
87/16 Susan SCHNEIDERand Roger DUNBAR
87/17 André LAURENT endFernando BARTOLOME
87/18 Reinh•rd ANCELMAR andChristoph LIEBSCHER
87/19 David BEGG andCharles VYPLOSZ
87/20 Spyros MAKRIDAKIS
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87/43 Jean GABSZEVICZ andJacques-F. TRISSE
87/44 Jonathan RAHILTON,Jacques-P. THISSEend Anita VESKAMP
87/45 Karel COOL.David JEMISON and
Ingemar DIERICKX
87/46 Ingemar DIERICKXand Karel COOL
1988
88/01 michael LAVRENCE andSpyros MAKRIDAXIS
88/02 Spyros MAKRIDAKIS
88/03 James TEBOUL
88/04 Susan SCHNEIDER
88/05 Charles VTPLOSZ
80/06 Reinhard ANGELMAR
88/07 Ingemar DIERICKX
and Karel COOL
88/08 Reinhard ANGELMAR
and Susan SCHNEIDER
88/09 Bernard SINCLAIR-
DESGAGNé
88/10 Bernard SINCLAIR.
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88/11 Bernard SINCLAIR-
DESGAGN6
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88/12 Spyros MAKRIDAKIS
88/13 Manfred KETS DE VRIES
08/14 Alain NOEL
88/15 Anil DEOLALIKAR andLars-Hendrik ROLLER
88/16 Gabriel HAVAVINI
88/17 Niehael BURDA
88/18 Michael BURDA
88/19 M.J. LAVRENCE andSpyros MAKRIDAKIS
88/20 Jean DERMINE,Damien NEVEM andJ.F. TRISSE
88/21 James TEBOUL
88/22 Lars-Hendrik ROLLER
88/23 Sjur Melk FLANand Georges ZACCOUR
88/24 8. Espen ECKBO and/kraft( LANGOHR
88/25 Everette S. GARDNERand Spyros MAKRIDAKIS
88/26 Sjur Didrik FLANand Georges ZACCOUR
88/27 Murugappe WUHANLars-Rendrik ROLLER
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' Équilibres de Nash-Cournot dans le marchéeuropéen du gaz: un cas où les solutions enboucle ouverte et en feedback colncident",Mars 1988
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88/30 Catherine C. ECKELand Theo VERMAELEN
88/31 Sumantra GHOSHAL andChrlstopher BARTLETT
88/32 Kasra FERDOVS andDavid SACKRIOER
88/33 Mihkel M. TOMBAK
88/14 Mihkel M. TOMBAK
88/35 Mihkel M. TOMBAK
88/36 V1kas TIBREVALA andBruce BUCHANAN
88/37
Murugappa KRISFINANLars-Hendrik ROLLER
88/18 Manfred KETS DE VRIES
88/39 Manfred MS DE VRIES
88/40 Josef LAKONISHOK andTheo VERMAELEN
88/41 Charles VYPLOSZ
88/42 Paul EVANS
88/43 B. SINCLAIR-DESGAGNE
88/44 Essais MAHMOUD andSpyros MAKRIDAKIS
88/45 Robert KORAJCZYKand Claude VIALLET
88/46 Yves DOZ andAmy SHUEN
'Oonaumer cognitive complexity and thediaensionality of aultidi gensional 'ratineconfigurations', May 1988.
' The financial felout from Chernobyl: riskperceptions and regulatory response, May 1988.
*Creation, adoption, and diffusion ofinnovations by subsidiaries of multinationalcorporations • , June 1988.
*International manufacturing: positioningplants for success', June 1988.
' The importance of flexibility Inmanufacturine, /une 1988.
' Flexibility: an important dimension inmanufacturIne, June 1988.
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"A Predictive Test of the N110 Nodal thatControls for Mon-stationarity*, June 1988.
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'The Leader as Mirror : Clinicol Reflections',July 1988.
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88/47 Alain BULTEZ,Els GIJSBRECHTS,Philippe NAERT andPiet VANDEN ABEELE
88/48 Michael BURDA
88/49 Nathalie DIERKENS
88/50 Rob VEITZ andArnoud DE NEYER
88/51 Rob VEITZ
88/52 Susan SCHNEIDER andReinhard ANCELMAR
88/53 Manfred KETS DE VRIES
88/54 Lars-Hendrik RÔLLERand Mihkel M. TOMBAI(
88/55 Peter BOSSAERTSand Pierre MILLION
88/56 Pierre MILLION
88/57 Wilfried VAN8ONACKERand Lydie PRICE
88/58 B. SINCLAIR-DESCACNEand Mihkel M. TOMBAI(
88/59 Martin KILDUFF
88/60 Michael BURDA
88/61 Lars-Hendrik OLIER
88/62 Cynthia VAN BULLE,Theo VERMAELEN andPaul DE VOUTERS
"Asymmetric cannibalise betveen substitut.items listed by retallers", September 1988.
"Reflections on 'liait uneeployment' inEurope, II", April 1988 revised September 1988.
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88/63 Fernando NASC/NF.Nr0and Wilfried R.VANHONAGKER
88/64 Kasra PERDOVS
88/65 Arnoud DE NETERand Kasra PERDOVS
88/66 Nathalie DIERKENS
88/67 Paul S. ADLER andKasra FERDOVS
1989
89/01 Joyce K. BYRER andTavfik JELASSI
89/02 Louis A. LE BLANCand Tavfik JELASSI
89/03 Seth H. JONES andTavflk JELASSI
89/04 Rasta FERDOVS andArnoud DE NEYER
89/05 Martin KILDUFP andReinhard ANCELMAR
89/06 Mihkel M. TOMBAI( andB. SINCLAIR-DESGAGNE
89/07 Damien J. NEVEN
89/08 Arnoud DE MEYER andRellmut SCHOTTE
89/09 Damien NEVEN,Carmen MATUTES andMarcel CORSTJENS
89/10 Nathalie DIERKENS,Bruno GERARD andPierre MILLION
"Strategie pricing of differentiated consumerdurables le e dynemic duopoly: e numeriealanalysie, October 1988.
"Charting ■trategic roles for internationalfactories", December 1988.
"Quality up, technology doms.", October 1988.
"A discussion of exact masures of informationassymetry: the exaeple of Niers and Milenodal or the importance of the asset structureof the firm", December 1988.
"The chief technology officer", December 1988.
"The iapact of language theories on DSSdialog*, January 1989.
"MS softvare selectiom: a multiple criteriadecisioa methodologe, January 1989.
"Megotiation supports the effects of computerintervention and confiant level on bargainingouteoee", January 1983:"Lasti ge leprovement in menufacturingperformance: I. seardh of a nev theory",January 1989.
"Shared history or shatved culture? The effectsof tige, culture, nad performance oninstitetionalizatiom te simulatedorganisation'", January 1989.
"Coordinating manufecturing and businessstrategles: I", February 1989.
"Structural adjustment in European retailbanking. Some vire from Industrialorganisation", January 1989.
'Trends in the development of technology andtheir effects on the production structure inthe European Comunity", January 1989.
"Brand proliferation and entry deterrence",February 1989.
"A market based approach to the valuation ofthe assets In place and the grog/thopportunities of the fine, December 1988.
89/11 Manfred RETS DE VRIESand Alain ROLL
89/12 VIlfried VAMIONACKER
89/11 Manfred KETS DE VRIES
89/14 Reinhard ANGES-NAM
89/15 Reinhard ANCELMAR
89/16 Vilfried 9ARHONACKER,Donald LEHNANN and SULTAN
89/17 Cilles AMADO,Claude FAuritEUX andAndré LAURENT
89/18 SrInI BALAK-RISUNAN andMitchell KOZA
89/19 Vilfrled VANYONACKER,Donald LEMANN and►areena SULTAN
•Understanding the leader- ttttt egy interface:application of the s elfe relationshipInterview nethoe, February 1989.
"Ratimatieg dynalet respoase nodale vben thedata are subject te different temporalaigre:ration', January 1989.
•The !aposter syndrome: e disquietingpbenomenem In organisation.' lite", February1989.
'Produc* innovation: • tool for competitiveadvantage• , Match 1989.
•tvaluatleg • fines product Innovationperfornaoce • . Narch 1989.
' Coebining related and 'parse data in linearrelreasloo modela • . February 1989.
' Changement organisationnel et réalitésculturelles, contrastes franco-américains•.Harth 1989.
' Information asyn•etry, market /silure andjoint-ventures: tbeory and evidence•.March 1989
•Cambiales releted and 'perse data in linearregvessioe Bodel'•,Revlsed March 1989
89/20 Vilfrled VANMONACKER "A ratioaal rendes behavior mode' of choice',and Russell RIPER
Revised March 1989
89/21 Arnoud de NETER andKasra FERDOVS
89/22 Manfred RETS DE VRIESand Sydney renov
89/21 Robert KORAJCZYR andClaude VIALLET
89/24 Martin K/LDUFF andMitchel ABOLAFIA
89/25 Roger 88TANCOURT andDavid CAUTSCH/
89/26 Charles BEAN,Edgeond MALINVAUD,rater 8ERNHOLZ,Francesco CIAVAllIand Charles VIPUDS2
•Influence et meavfactoring improvementprogrammes on performance • , April 1989
•vhat is the sole of character InpsychomalysisT April 1989
"Bquity tisk presle and the pricing of fore1gnexchange tisk • April 1989
' The social destruction of reality:Organisation.' con/net as social drameApril 1989
"Tvo esaential charecteristics of retailmarkets and ther etoncalc consequences"March 1989
'Maccoeconoeic policies for 1992: thetransition and atter • , April 1989
89/27 David KRACKRARDT andMartin KILDUFP
89/28 Martin RILDUFF
89/29 Robert COCEL andJean-Claude LARRECRE
89/30 Lars-Bendrik ROLLERand Nikkei M. TOMBAK
89/31 Nichael C. BURDA andStefan GERLACO
89/32 Peter RAM andTawfik JELASSI
89/33 Bernard SINCLAIR-DESCACNE
89/34 Su.antra GHOSBAL andNittin NOIIRIA
89/35 Jean DERNINE andPierre BILLION
89/36 Martin KILDUPF
89/37 Manfred RETS DE VRIES
89/38 Manfrd RETS DE VRIES
89/39 Robert KORAJCZTR andClaude VIALLET
89/40 Halait CBAKRAVARTET
89/41 B. SINCLAIR-DESGACNEand Nathalie DIERRENS
89/42 Robert ANSON andTavfik JELASSI
89/43 Nichael BURDA
89/44 BalajiCRAKRAVARTIffand Peter LORANGE
89/45 Rob VEITZ andArnoud DE METER
"Friendship patterns and cultural attributions:the control of organisational divereity".April 1989
*The interpersonal structure of decisionnaking: • social comparison approach toocganiaational choke", Revised April 1989
•The battlefield for 1992: product strengthand geographic coverage*, Nay 1989
•Competition and Investment in FlexibleTechnologies• , May 1989
•Durables and the US Trade Deficit*, May 1989
•Application and ovalisation of a multi-criteriadecision support system for the dynanicselection of U.S. manufacturiug locations•,May 1989
•Design flexibility in monopsonisticindustries• , Nay 1989
*Requisite variety verses shared values:nanaging corporate-divinion relationahipa inthe M-Form organisatime, May 1989
•Osposit rate caillas* end the market value ofbanks: The case of Femme 1971-1981 • , May 1989
wA dispositiomal appreatà to social netvorks:the case of organixational choire• , May 1989
*lhe organisational foel: balancine . a leader'shubria*, May 1989
"The CR0 blues', June 1989
"An enpirical investigation of internationalasset pricine, (Revised June 1989)
'Management systems for innovation andproductivite, June 1989
'The strategic supply of precisions • , June 1989
"A deve/opment franevork for computer-supportedconflict resolution*, July 1989
"A note on firing costs and severance benefitsin equilibriun unenploynent*, June 1989
"Strategic adaptation in nulti-business firme,June 1989
altanaging expert systems: 4 franevork and casestudy", June 1989
89/46 Marcel CORSTJENS,Carmen MATUTES and
"Entry Encouragement", July 1989
Damien NEVEN
89/47 Manfred KETS DE VRIES "The global dimension in leadership andand Christine MEk0 organization: issues and controversies",
April 1989
89/48 Damien NEVEN andLars-Hendrik ROLLER
"European integration and trade flovs",August 1989
89/49 Jean DERMINE "Some country control and mutuel recognition",July 1989
89/50 Jean DERMINE "The specialization of financial institutions,the BEC model", August 1989
89/51 Spyros MAKRIDAKIS "Sliding simulation: a nev approach to Umeseries forecasting", J uly 1989
89/52 Arnoud DE MEYER "Shortening developmen t cycle times: amanufacturer's perspec tive", August 1989