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This article introduces this JBR Special Issue on simple versus complex methods in forecasting. Simplicity in forecasting requires that (1) method, (2) representation of cumulative knowledge, (3) relationships in models, and (4) relationships among models, forecasts, and decisions are all sufficiently uncomplicated as to be easily understood by decision-makers. Our review of studies comparing simple and complex methods - including those in this special issue - found 97 comparisons in 32 papers. None of the papers provide a balance of evidence that complexity improves forecast accuracy. Complexity increases forecast error by 27 percent on average in the 25 papers with quantitative comparisons. The finding is consistent with prior research to identify valid forecasting methods: all 22 previously identified evidence-based forecasting procedures are simple. Nevertheless, complexity remains popular among researchers, forecasters, and clients. Some evidence suggests that the popularity of complexity may be due to incentives: (1) researchers are rewarded for publishing in highly ranked journals, which favor complexity; (2) forecasters can use complex methods to provide forecasts that support decision-makers’ plans; and (3) forecasters’ clients may be reassured by incomprehensibility. Clients who prefer accuracy should accept forecasts only from simple evidence-based procedures. They can rate the simplicity of forecasters’ procedures using the questionnaire at
Simple versus complex forecasting: The evidence
Kesten C. Green, and J. Scott Armstrong
March 2015
This article introduces the Special Issue on simple versus complex methods in
forecasting. Simplicity in forecasting requires that (1) method, (2) representation of
cumulative knowledge, (3) relationships in models, and (4) relationships among models,
forecasts, and decisions are all sufficiently uncomplicated as to be easily understood by
decision-makers. Our review of studies comparing simple and complex methods
including those in this special issuefound 97 comparisons in 32 papers. None of the
papers provide a balance of evidence that complexity improves forecast accuracy.
Complexity increases forecast error by 27 percent on average in the 25 papers with
quantitative comparisons. The finding is consistent with prior research to identify valid
forecasting methods: all 22 previously identified evidence-based forecasting procedures are
simple. Nevertheless, complexity remains popular among researchers, forecasters, and
clients. Some evidence suggests that the popularity of complexity may be due to incentives:
(1) researchers are rewarded for publishing in highly ranked journals, which favor
complexity; (2) forecasters can use complex methods to provide forecasts that support
decision-makers’ plans; and (3) forecasters’ clients may be reassured by
incomprehensibility. Clients who prefer accuracy should accept forecasts only from simple
evidence-based procedures. They can rate the simplicity of forecasters’ procedures using
the questionnaire at
Keywords: analytics; big data; decision-making; decomposition; econometrics; Occam’s
This paper is forthcoming in Journal of Business Research in 2015. This working paper
version is available from
Acknowledgements: Kay A. Armstrong, Ron Berman, John E. Boylan, Peter Fader,
Antonio García-Ferrer, Robert Fildes, Paul Goodwin, Wilpen Gorr, Andreas Graefe, Robin
M. Hogarth, Xueming Luo, Philip Stern, Aris Syntetos, Christophe van den Bulte, and
Malcolm Wright provided helpful reviews. We are grateful to the many authors we cite
who replied to our appeal for help, suggested improvements to our summaries of their
research, and pointed us to additional evidence. Hester Green, Emma Hong, Sue Jia, Yifei
Pan, and Lynn Selhat edited the paper. The authors of this article are responsible for any
remaining errors or omissions.
Contact information: Kesten C. Green, University of South Australia Business School,
and Ehrenberg-Bass Institute, GPO Box 2471, Adelaide, SA 5064, Australia; J. Scott Armstrong, The Wharton School, University of
Pennsylvania, 700 Huntsman Hall, 3730 Walnut Street, Philadelphia, PA 19104, U.S.A.,
and Ehrenberg-Bass Institute, Adelaide;
1. Introduction
This article provides an introduction to this Special Issue on simplicity in forecasting.
The call for papers was subtitled “Conditions and complexity in forecasting,” and the
objective was to publish “research to improve forecasting knowledge by comparing the
usefulness of simple and complex alternatives under different conditions.”
A trend toward complex forecasting has been underway for the past half-century or
more. Econometricians who believe that complex statistical procedures yield greater
forecast accuracy have led the trend (see, e.g., Armstrong 1978). The trend is at odds with
the common belief among scientists that scientists should strive for simplicity. The
preference for simplicity in science can be traced back to Aristotle (Charlesworth, 1956),
and is commonly identified with the 14th Century formulation, Occam’s razor. Indeed
“since that time, it has been accepted as a methodological rule in many sciences to try to
develop simple models” (Jensen 2001, p. 282). Zellner (2001) concludes social scientists
too should strive for simplicity. He was joined in this conclusion by the 21 authors
contributing to the book, Simplicity, Inference and Modelling (Zellner, Keizenkamp, and
McAleer, 2001).
This article first draws upon prior literature to develop an operational definition of
simplicity in forecasting, then uses the definition to identify and analyze comparative
studies that could be expected to provide evidence on the conditions under which
complexity is useful. The review of studies includes new evidence presented in this Special
Issue. Finally, this article examines evidence on why researchers, forecasters, and decision-
makers are, despite the theoretical and empirical objections, attracted to complexity.
2. Defining simplicity in operational terms
Simplicity in forecasting seems easy to recognize, yet is difficult to define. The first
definition in the Oxford English Dictionary’s OED Online (2014) is, nevertheless, a useful
starting point: “The state or quality of being simple in form, structure, etc.; absence of
compositeness, complexity, or intricacy.
For the purpose of making practical distinctions between simple and complex
forecasting, this article defines simple forecasting as processes that are understandable to
forecast users. Specifically, the forecasting process must be understandable with respect to
methods, representation of prior knowledge in models, relationships among the model
elements, and relationships among models, forecasts, and decisions.
Complexity in forecasting is the opposite of simplicity. In contrast to some discussions
of complexity in forecasting, by our definition complexity is not a function of the number
of variables. Nor is complexity a function of the effort required to develop a model.
To conclude whether or not an instance of forecasting is simple, as defined here, ask
forecast users if they understandand, if so to explainthe forecasting method, how the
specific model represents prior knowledge, how any parts the model has are related to each
other, and how and why a forecast from the model would help them to make a better
decision. A structured questionnaire to derive a measure of the simplicity of the forecasting
procedures from forecast usersunderstandingthe Forecasting Simplicity
Questionnaireis available from
The test of simplicity provided by the questionnaire has face validity. Recounting his
correspondence with Nobel Laureates and other leading economists, Zellner reports James
Tobin telling him that he and his Council of Economic Advisors colleagues were skeptical
of complex models of the economy because they “could not understand the workings and
outputs of such models, and thus did not have much confidence in them” (Zellner 2001, pp.
Zellner (2001, p. 242) observes, “Some years ago, I came upon the phrase used in
industry, ‘Keep it simple stupid’, that is, KISS, and thought about it in relation to scientific
model-building. Since some simple models are stupid, I decided to reinterpret KISS to
mean ‘Keep it sophisticatedly simple.’” With that in mind, this article is concerned
primarily with comparisons of complex forecasting with simple forecasting procedures that
have been validated by experimental comparisons.
2.1. Simple methods
Simple forecasting methods are relatively few compared to complex methods, which are
limited in number only by the imaginations of statisticians. The titles and abstracts of
forecasting papers in academic journals attest to the proliferation of complex methods. Not
only managers, but also practitioners and many researchers are also likely to struggle to
comprehend typical forecasting papers.
Incomprehension of forecasting methods, even by the people who pay for them, seems
common. For example, as part of a three-person consulting team, the second author of this
article interviewed several analysts in a large firm to assess their understanding of a
complex model provided at high cost by an outside vendor. The model was designed to
forecast the effects of advertising expenditures on the company’s market share. The vendor
provided courses to explain the method to their clients. Even so, none of the analysts could
explain how the model worked (Armstrong and Shapiro, 1974).
2.2. Simple representation of prior knowledge in models
A scientific, or evidence-based, approach to forecasting requires an effort to summarize
cumulative knowledge (Armstrong, Green, and Graefe, this issue). Before the 1970s,
econometricians often based their forecasting models on a priori analyses. They used
domain experts’ knowledge and what evidence they could glean from prior research to
guide their selection of variables, to determine directions and the nature of the relationships,
and to estimate the magnitudes of the relationships. While the process is a logical scientific
procedure and is simple to explain, much time and effort by experts is often required in
order to carry it out.
In contrast to the high cost of a thorough a priori analysis, applying complex statistical
methods to large databases is inexpensive. McCloskey and Ziliak (1996) and Ziliak and
McCloskey (2004) show that many researchers follow the low-cost approach. Their
analyses of American Economic Review papers found that 75 percent of the papers in the
1980s that used regression analysis went beyond statistical significance to consider other
information when selecting variables for regression models. The figure dropped to 32
percent in the 1990s.
Regression analysis identifies statistical patterns in a particular set of data. If the data
are non-experimental, no matter how “big” they are, there is little reason to expect the
process to identify causal relationships (Armstrong 2012; Armstrong, Green, and Graefe,
this issue). In practice, a big data set is likely to include variables that are not independent
of one another, variables that vary little or not at all, and irrelevant variables, while
excluding variables that are important. The need for theory, domain knowledge,
experimental data, and careful thinking for specifying and estimating causal models has not
Bayes’ method provides another way to incorporate prior knowledge in forecasting
models. The method has the disadvantage of being too complex for most people to
understand. We have been unable to find evidence that Bayesian approaches yield ex ante
forecasts that are more accurate than forecasts from simple evidence-based methods. The
first M-Competition (Makridakis, Anderson, Carbone, Fildes, Hibon, Lewandowski,
Newton, Parzen, and Winkler, 1982) includes tests of Bayesian forecasting for 1 to 18
period ahead forecasts for 997 time series. Forecasts from simple methods, including naïve
forecasts on deseasoanlized data, were more accurate than Bayesian forecasts on the basis
of mean absolute percentage error (MAPE). Forecasts from the benchmark deseasonalized
single exponential smoothing method reduced error by 12.4 percent (from Makridakis et al.,
1982, Table 2a). Bayesian forecasts were not included in subsequent M competitions.
Graefe, Küchenhoff, Stierle, and Riedl (2014) found that simply averaging forecasts from
different methods yields forecasts that reduced error by an average of 5 percent across five
studies compared to those from Bayesian approaches to combining economic and political
forecasts. Goodwin (this issue) demonstrates that for many forecasting problems that
involve choosing between two alternatives, two simple methods would each lead to the
same decision as Bayes’ method.
The simplest representations of prior knowledge in forecasting models are no-change
models. Forecasts from appropriately formulated no-change models are hard to beat in
many forecasting situations, either because prior knowledge is insufficient to improve on
no-change or because prior knowledge leads to the conclusion that the situation is stable.
2.3. Simple relationships among the model elements
Decomposition provides a path to simplicity for many forecasting problems.
Decomposition in forecasting consists of breaking down or separating a complex problem
into simpler elements before forecasting each element. The forecasts of the elements are
then combined.
Some researchers suggest that decomposition increases complexity relative to
forecasting the aggregate directlysuch as the works cited by Brighton and Gigerenzer in
this issuebut that is not the case with the definition proposed in this article.
Decomposition is a key strategy for simplifying problems in management science, and
in other scientific fields. Decomposition can be used with any forecasting method. The
method is most useful when different elements of the forecasting problem are forecast by
different methods, when there is valid and reliable information about each element, the
elements are subject to different causal forces, and when they are easier to predict than the
A study on forecasting traffic accidents by García-Ferrer, de Juan, and Poncela (2006)
provides evidence on the benefits of disaggregation when these conditions are met. Their
approach of disaggregation by estimating separate models for urban and other roads
produced forecasts that were more accurate for between 76 and 85 percent of the 63
comparisons, depending on the criterion used.
If there are few data on each element, however, decomposition may not improve
forecast accuracy. Huddleston, Porter, and Brown (this issue) examine the trade-off in their
tests of different approaches to forecasting highly variable district-level burglary rates.
The relationships among the elements of the decomposed problem should be simple.
Decomposition based on additive relationships, an approach that is often referred to as
segmentation, is ideal. Decomposition based on multiplicative relationshipsin which the
elements are multiplied together to obtain a forecast of the wholeis somewhat more
complex, carrying the risk that errors will multiply; nevertheless, multiplicative
decomposition is often useful for simplifying complex problems.
Many ways are available to decompose forecasting problems. A common approach to
forecasting sales, for example, is to forecast market size and market share separately.
Another approach is to decompose a time-series by estimating the starting level
“nowcasting”and forecasting the trend separately. Combining nowcasting with trend
forecasting is an old idea that does not appear to be widely used, and comparative tests are
few. Nevertheless, the two studies described in Tessier and Armstrong (this issue) suggest
that substantial error reduction is possible.
Transforming variables can help to avoid complexity in a model. Perhaps the most
common approach is to transform multiplicative relationships into additive relationships by
using logarithms. The coefficients of variables in logarithmic form are known as elasticities.
Elasticities represent relationships in an easily understood and useful way; they are the
expected percentage change in the variable being forecast arising from a one percent
change in the causal variable. The intuitiveness of elasticities allows clients to readily
transform their knowledge into expectations about the magnitude of causal relationships.
The index method is an approach to decomposition that is appropriate for situations with
many causal variables. The index method involves identifying and examining each causal
relationship individually before combining them in a forecasting model. This easily
understood approach avoids the complications that arise from using regression analysis to
develop a forecasting model. As Armstrong, Green, and Graefe (this issue) describe, index
models provide forecasts of advertising effectiveness and election results that are
substantially more accurate than those from multiple regression models.
2.4 Simple relationships among models, forecasts, and decisions
The relationships among the models, forecasts, and decisions need to be clear to
decision-makers in order to help them to choose among alternative courses of action. One
way to achieve that clarity is to describe the proposed method, and then ask the decision-
makers what decisions they would make in response to different hypothetical forecasts. The
forecasts should include forecasts of costs and benefits, and likelihoods. Hogarth and Soyer
(this issue) found that forecast users make better use of uncertainty information about
forecasts when they are able to observe possible outcomes with the aid of simulation
software, than when they are provided with standard statistical information about the model.
Indeed, the complex statistics typically provided with regression models are unlikely to
help decision-makers to make better decisions, as they confuse even statisticians. Soyer and
Hogarth (2012) ask 90 economists from leading universities to interpret standard regression
analysis summaries. Roughly two-thirds of their answers to three relevant questions were
substantively wrong.
Regression statistics can divert attention from the decision-makers need to assess the
effects of causal variables. Regrettably, the attention of decision-makers is commonly
subject to diversion of that kind. Academics are not immune, as Ziliak and McCloskey
(2008) show with many examples from econometric forecasting.
23!.*+!4-+!2@!,"<!/37!@037-!60..6+!;+6/.023-*0=!>0.*!@2;+1/-.!/114;/18C!Similarly, Peach
and Webb (1983) estimate 50 econometric models in each of three standard mathematical
forms using 95 and 134 observations. The models involved three independent variables and
one dependent variable chosen at random from the National Bureau of Economic
Research’s data bank. The resulting ," and t statistics were similar to those of established
models published in the economics literature. L@@2;.-!B8!@2;+1/-.+;-!.2!05=;2A+!," are
likely to harm predictive validity because each new model specification leads the modeler
away from the original theoretical formulation, assuming there was one.
Ziliak and McCloskey (2008) illustrate the harm caused by statistical significance
testing with examples taken from across the sciences. Cumming (2012) describes
additional examples. Much of the harm caused by tests of statistical significance arises
because they divert attention from the pursuit of important information, such as the likely
costs and benefits of a proposed policy. For example, Hauer (2004) reports that the use of
statistical significance led to poor decisions on automobile traffic safety policy, such as the
right-turn-on-red rule. Forecasts of the effects of the rule on accidents and deaths, and the
time saved by drivers, would have been more useful than the results of statistical
significance tests.
Simpler and more useful measures are available to forecasters than R2 and statistical
significance. For example, to assess which forecasting method is best, the relative absolute
error (RAE)being the size of the forecast error relative to the size of the forecast error
from a relevant no-change modelis useful and simple to understand. For production and
inventory control decisions, the mean absolute error (MAE) is a simple and useful measure
(Armstrong and Collopy, 1992), although it can mislead if demand is intermittent (Boylan
and Syntetos 2006; Teunter and Duncan 2009).
3. Effects of complexity of methods and models on accuracy
Simplicity in forecasting has the obvious advantage of encouraging engagement and
criticism by facilitating understanding. In addition, simplicity aids in detecting mistakes,
important omissions, ludicrous variables, unsupported conclusions, and fraud. But how
accurate are simple methods?
To answer that question, the authors of this article searched for studies that compare the
accuracy of forecasts from simple versus complex forecasting procedures. To do so, they
used keywords to search for papers on the Internet, examined references in key studies, and
contacted key authors. The emphasis of the search was on finding studies showing that,
under certain conditions, complex methods provide forecasts that are more accurate. To
help ensure that accurate representation of the studies identified in the search and reduce
the risk of overlooking important studies, the authors attempted to contact the living
authors of papers cited in substantive ways in this article. Twenty-one out of the 27 authors
with known email addresses responded. Their replies led to improvements in the paper. The
authors of one paper disagreed with the analysis of their findings on forecasts from neural
networks presented in this article. Details of the analysis are available at simple-, along with a statement by the two authors of their own conclusions about
their study.
When this article was near completion, the authors sent drafts to email lists with
requests for further evidence, especially evidence that conflicts with the article’s
conclusions. Responses provided opinions for and against the conclusions along with a few
references to relevant studies. The request led to few additions to the evidence because the
studies proposed by respondents did not provide evidence on complexity versus simplicity
as the concepts are defined in this article. Typically they associated complexity with the
number of variables, a factor explicitly excluded from this article’s definition.
The following sections review the evidence on simplicity versus complexity for
judgmental, extrapolative, and causal methodsand for combining forecasts. In the
judgement of the authors of this article, the differences in the complexity of the methods in
the comparative studies identified were typically large, though the simpler methods were
often not as sophisticatedly simple as as they might have been. In other words, the
comparisons we identify may well understate the relative difference in performance
between complex and simple evidence-based methods. Full disclosure of ratings is
provided at so that readers can make their own judgments.
3.1. Judgmental methods
Humanscapacity for mental processing of information has modest limits. As a
consequence, judgmental forecasters rapidly reach a point beyond which further
information does not help them to make more accurate forecasts. Moreover, humans, no
matter how clever, are unable to learn about complex relationships from experience alone.
Thus, without structured methods, we are all ill equipped to make forecasts about complex,
uncertain situations.
The structure, however, need not be complex. In a study on forecasting demand for a
new form of transportation, a quasi-experiment compares complex and simple methods for
obtaining data on purchase intentions. Subjects in the complex treatment visited a product
clinic that allowed them to sit in a prototype car, see descriptive wall posters, watch a
descriptive movie, and participate in a focus group. Then they completed an intentions
survey. Another group was mailed a two-page description of the system, the second page
being a picture of the prototype car, and participants completed the same intentions survey.
The reported intentions were similar for the two groups (Armstrong and Overton, 1971).
Lees and Wright (2004) provide further evidence on the effects of additional
information on intentions surveys. They obtained purchase intentions for five diverse
product concepts. The proposed products were presented in one of three forms: simple
factual description, extended promotional description, and extended promotional
description with artwork. They obtained responses from between 565 and 625 respondents
per treatment, and find little difference in intentions to purchase between those who had
been given the simple descriptions and those given more complex descriptions.
Simulated interaction provides a simple way to structure comprehensive information
about complex situations that involve interactions between parties whose interests diverge.
The method involves asking people to take on the roles of key participants, providing them
with a short description of the situation, and leaving them to interact in ways that are
appropriate to the situation. The typical decision reached in a simulated interaction is used
as the forecast. Green (2005) obtained 105 simulated interaction forecasts of decisions in
eight conflict situations. The forecasts reduced error by 47 percent compared to the 101
forecasts by experts on the complex method of game theory
The interactions in the simulated interaction method appear to enable people to make
better use of more information about complex situations than is the case with unaided
judgment. Green and Armstrong (2011) test that assumption by obtaining 101 role-
thinking forecasts of the decisions that would be made in nine diverse conflicts from 27
Naval postgraduate students and 107 role-thinking forecasts from 103 novices. Given the
complex task of thinking about the roles, objectives, strategies, and interactions of the
parties in conflict situations, the accuracy of both groups’ forecasts was little better than
the 28 percent correct that could be expected from guessing. Thus, neither experts nor
novices were able to make good use of information about complex situations by thinking
hard about them, whereas the same information could be simply and realistically modeled
by simulated interaction, the use of which reduced forecast error by 41 percent for the
nine situations.
3.2. Extrapolation methods
Extrapolation methods that incorporate more data are likely to improve forecast
accuracy. That said, more recent data are typically more relevant, especially for short-term
forecasts. To address that dilemma, Brown (1956) proposes exponential smoothing.
Exponential smoothing forecasts turned out to be more accurate than those from commonly
used methods such as judgmental extrapolation and moving averages, and the additional
complexity that arises from using exponential smoothing is trivial.
A second sophisticatedly simple improvement to extrapolation involves damping the
trend in an exponential smoothing model toward zero when there is uncertainty (see
Gardner 2006 for a review). By our definition, damping only trivially increases complexity.
All is done automatically via decomposition, along with additions and multiplications.
A third sophisticatedly simple improvement to extrapolation is achieved by making
adjustments for seasonality when the interval of forecasts is shorter than one year. The now
widespread use of seasonal factors is largely influenced by the work of Shiskin (1965).
Seasonal adjustment is a form of decomposition, and can be implemented using addition or
multiplication. Seasonal adjustments can reduce forecast errors substantially. For example,
for 68 monthly economic series from the M-Competition, Makridakis et al. (1982, Table
14) found that seasonal adjustments reduced the MAPE of forecasts for horizons out to
18 months from 23.0 to 17.7 percent—a 23 percent error reduction. In the M2
Competition, seasonal adjustment reduced MAPEs for 23 monthly series forecast for up to
15 months ahead by 41 percent (from Exhibit 1, Makridakis, Chatfield, Hibon, Lawrence,
Mills, Ord, and Simmons, 1993).
The simple no-change extrapolation model is a strong competitor in many forecasting
situations, often after the data have been decomposed or adjustede.g., by or for price
level or population. The model is usually formulated as “no change from the current level”
but sometimes as “no change from the long-term trend.” A well-known demonstration of
the power of the no-change model is the “random walk down Wall Street” (Malkiel, 2012).
Random walk is an economists’ term to describe the behavior of a time series without a
predictable pattern, and hence the next value in the series is expected to be the same as the
previous one. Researchers have been unable to improve upon the no-change model for
forecasting day-ahead prices in the stock market.
Similarly, Schnaars and Bavuso (1986) compare the accuracy of 180 forecasts from the
no-change model with 180 forecasts from each of six more complex extrapolation methods
applied to each of 15 weekly economic indicators. The indicators included production,
unemployment claim, and resource price series. On average, the no-change model yielded
the most-accurate forecasts. The forecast errors, MAPEs, from the no-change model were
half those of forecasts from the most complex extrapolation method tested, generalized
adaptive filtering.
Over the past seven decades or so, authors of journal articles have proposed many
complex extrapolation procedures. An early review of comparative studies suggests they
have not lead to improvements in the accuracy of forecasts, with 28 comparisons finding
forecasts from the simpler method were as or more accurate than those from the more
complex method and only 11 finding better accuracy from the more complex method
(Armstrong, 1984).
Research since the 1984 review provides additional evidence. Smith’s (1997) review
found six studies in which extrapolations of population from complex models were no
more accurate than those from simpler models, and only one study in which complex
models were more accurate. The simple method was not, however, sophisticatedly simple.
Studies in marketing have shown similar results. Schnaars (1984) and Meade and Islam
(2001) found that forecasts from complex curve-fitting models were no more accurate than
those from simple extrapolation models. And in their review of evidence on methods for
forecasting the trial of new consumer packaged goods, Fader and Hardie (2001) report that
extrapolations using simple modelswhich were based on estimates of propensities to buy
from early purchase dataprovide more accurate forecasts than those from complex
models estimated from the same data in two comparisons. Brighton and Gigerenzer (this
issue) describe findings that experts’ simple rules provide forecasts of customer behavior
that are more accurate than mathematically sophisticated models advocated by researchers.
The M-Competition found that the simplest extrapolation methods suitable for the data
used in the competitiondeseasonalized no-change and single exponential smoothing
provided forecasts that were at least as accurate than those from all 16 of the more complex
methods. On average, the two simplest methods provided forecasts for 1 to 18 months
ahead for 1,001 time series that reduced MAPE by 34 percent compared to the forecasts
from the more complex methods (from Table 2a, Makridakis et al., 1982). In the M2
Competition, the deseasonalized no-change and combined exponential smoothing forecasts
reduced MAPE by 27 percent on average compared to forecasts from seven more-complex
methods; namely five expert forecasters who had access to causal information, Box-Jenkins,
and an autoregressive model (Exhibit 1 from Makridakis et al., 1993). In the case of the M3
Competition, the deseasonalized no-change, combined exponential smoothing, and Rule-
Based Forecasting forecasts reduced MAPE by nearly 1 percent on average compared to
forecasts from 17 more complex methods (Table 6 from Makridakis and Hibon, 2000). The
relatively modest error reduction from the simpler methods in the M3 Competition
presumably arises because the contestants learnt that naïve forecasts, exponential
smoothing, and damping are hard to beat and, as a result, more contestants entered
forecasts drawn from these methods via expert systems and proprietary software, and fewer
of the complex forecasting methods that have failed badly were entered.
Forecasts from neural networks, a complex method, were 3.4 percent less accurate than
relatively simple damped-trend forecasts in a test against 3,003 series in the M3-
Competition (Makridakis and Hibon, 2000). In Crone, Hibon, and Nikolopoulos’s (2011)
subsequent forecasting competition, competitors entered forecasts from 27 methods22 of
which were neural network methodsfor 1 to 18 month horizons for either 11 or 111
monthly time series. The competition organizers included forecasts from six methods that
are simple using this article’s definition. They are the naïve or no-change model without
seasonal adjustment, seasonal adjustment, single exponential smoothing, Holt’s exponential
smoothing, dampened exponential smoothing, and a simple average of the exponential
smoothing forecasts. The median RAEs of forecasts from the six simple methods are 9.9
percent smaller than the median RAEs of the forecasts from the 22 neural network methods
and 8.5 percent smaller than the median RAEs of the forecasts from all 27 of the complex
methods entered in the competition when compared using geometric means. Moreover, the
typical neural network forecast was four percent less accurate than forecasts from the naïve
(no-change) model.
For another example, consider the task of forecasting intermittent demand. Syntetos,
Babai and Gardner (this issue) compare forecasts from simple, no trend, exponential
smoothing and two other simple techniques developed specifically for intermittent demand
forecasts, with those from a complex method reported by Willemain, Smart, and Schwarz
(2004). They find little difference in the forecasts for jewelry sales, and forecasts from the
complex method were not as useful as those from simple exponential smoothing for
electronics sales.
Nikolopoulos, Goodwin, Patelis, and Assimakopoulos (2007) compare methods for
forecasting audience shares for a holdout sample of 12 TV sporting events. A simple
average of the shares obtained by the five most analogous TV shows, from among 34
previous shows, reduced error by 31 percent compared to the average errors of forecasts
from two multivariate regression and three neural network models. Their forecasts based on
three analogies and one analogy are not as accurate as those based on five, which is
consistent with the findings of Green and Armstrong (2007), and suggests why Brighton
and Gigerenzer’s (this issue) “single nearest neighbor” analogy forecasts perform relatively
poorly in their test of methods for picking the city with the larger population of German
city pairs: they used only a single analogy.
In another example of extrapolating from analogous data, Wright and Stern (this issue)
compare the accuracy of sales forecasts for very different new products. The simpler, more
intuitive method based on the sales of analogous products provided forecasts that were
substantially more accurateerror was reduced by 43 percentthan the forecasts from
three established complex models. Wright and Stern note that the established complex
models are, in turn, simpler than four other models that were rejected in prior research due
to the relative inaccuracy of their forecasts.
3.3. Causal methods
Causality is often complex. As a consequence, people often assume that complex
methods and models will be needed for forecasting. Lesser (1968) observes that
econometricians strive for complexity by using more equations, more complex functional
forms, and more complex interactions in their regression models. Consistent with this, a
survey of leading econometricians by Armstrong (1978) finds that the great majority of the
21 respondents agree with the proposition that more complex econometric methods will
provide more accurate forecasts. A study on the accuracy of short-term economic forecasts
by the National Bureau of Economic Research in the early 1970s concludes that, “the
record reveals no clear-cut and sustained advantage of complex… forecasting systems”
(Juster 1972, p. 23).
As early as the mid-1900s, econometricians proposed that simultaneous equations
which are complicated because they involve interactions among the equationsshould lead
to more accurate forecasts than simpler approaches. Armstrong (1985) found five
comparative studies; the use of simultaneous equations failed to improve accuracy in any of
them (p. 200).
Nikolopoulos, Goodwin, Patelis, and Assimakopoulos (2007) find that a simple one-
causal-variable regression model, estimated from 34 observations, reduces the error of
audience share forecasts by 37 percent, compared to forecasts from two more-complex
regression models using the same data. One of the complex models incorporated all three
available causal variables and the other was a stepwise regression model incorporating the
best two variables, based on correlations. The simple model also provided an error
reduction of 22 percent compared to the average of the forecast errors from three neural
network models.
Fildes, Wei, and Ismail (2011) compared conditional one, two, and three-year forecasts
of air passenger traffic flows from ten complex econometric models with exponential
smoothing forecasts. Compared to the average complex econometric forecast, exponential
smoothing forecasts reduced error across all horizons and overall by 10.8 percent on the
basis of geometric RAE (from Fildes, Wei, and Ismail, 2011, Table 6). Despite the fact that
the econometric models use more information, the complexity penalty led to increased
forecast errors.
The case for simple econometric methods became stronger when evidence on the value
of equal-weights began to appear in the 1970s (e.g. Schmidt, 1971). Empirical evidence
shows that simply assigning equal-weights to standardized predictor variables in a linear
model usually yields ex ante forecasts that are at least as accurate as those from methods,
such as regression analysis, that calculate optimal fits with the estimation data (see Graefe,
this issue, for a review of the evidence).
Woike, Hoffrage, and Petty (this issue) provide further evidence on the advantages of
uncomplicated weighting methods in their simulations of venture capital investment
decisions. Their simpler weighting schemes provided predictions that led to more profitable
decisions in most environments and provided the most reliable predictions when the
environment was uncertain.
The Dean of North Dakota College of Pharmacy asked Gorr, Nagin, and Szczypula
(1994) to develop a better model for forecasting prospective students’ final GPAs. The
college used a model consisting of a simple judgmentally weighted index of seven
variables. Alternative models based on multiple regression, stepwise regression, and
artificial neural networks provided no meaningful improvements in accuracy.
Graefe (this issue) examines evidence from U.S. presidential election forecasting. The
ex ante forecast errors from versions of nine established regression models that equally
weighted the causal variables were five percent smaller than those from the original models.
In addition, Graefe demonstrates one of the major advantages of a simple additive equal-
weights approach: the ability to include all variables that are important in a causal model.
The error of ex ante forecasts from an equal-weights model that included all of the 27
unique causal variables from the nine original models was 48 percent lower than the error
of the typical model and 29 percent lower than the error of the forecasts from the most
accurate regression model.
3.4. Combining forecasts
Combining forecasts that incorporate different data and knowledge is a simple and
easily understood way to represent prior knowledge. In a point of departure with Brighton
and Gigerenzer (this issue), we regard combining as being an inherently simple forecasting
procedure in keeping with the definition proposed in this article.
Complex methods for averaging have been proposed, but have not been met with
success. An examination of Clemen's (1989) review of 209 studies on combining forecasts
suggests that complex combining schemes cannot be relied upon to provide forecasts that
are more accurate than those from simple averages. Studies since 1989 support Clemen’s
conclusion. For example, Duncan, Gorr, and Szczpula (2001, p. 209 Exhibit 6) find that
using a complex method for combining forecasts of school revenues from a complex
forecasting method increases forecast errors from 5.5 to 10.7 percent, or by 94 percent.
Lyon, Wintle, and Burgman (this issue) elicit confidence intervals for estimates of 311
quantities from 264 participants in 15 experiments. They test 13 complex approaches to
combining the subjects’ confidence intervals, and find that simple trimmed-means provide
the most accurate point forecasts. Graefe, Küchenhoff, Stierle, and Riedl (2014) find that
for economic forecasting and election forecasting, the simple average provided more
accurate predictions than did a Bayesian approach to combining in five comparisons, and
somewhat less accurate forecasts in one comparison.
Fildes and Petropoulos (this issue) provide evidence on forecasting method selection for
combinations. Their findings support differential weighting in situations when there is prior
evidence on which methods provide forecasts that are most accurate given the conditions.
4. Why simplicity repels and complexity lures
For what reasons do forecasters avoid simplicity? One is that if the method is intuitive,
reasonable, and simple, would-be clients might prefer to do their own forecasting.
Another reason is that complexity is often persuasive. The “Dr. Fox study” found that
university faculty and staff gave high ratings to a complex lecture, even though the content
was nonsensical. Respondents commented that while they did not understand everything Dr.
Fox said, he certainly “knew his stuff” (Naftulin, Ware, and Donnelly 1973). An extension
by Armstrong (1980) describes tests using simple and complex versions of papers with
identical content. Academicians rated the authors of research papers more highly when the
papers were written in more complex ways. For additional experimental evidence, see
Armstrong (2010, pp. 183184).
Eriksson’s (2012) experiment provides additional evidence on the persuasiveness of
complexity. The experiment included showing abstracts of two published papers to 200
subjects, all of whom were familiar with reading research reports and had post-graduate
degrees. One of the abstracts includes a sentence from an unrelated paper that contains an
algebraic equation. Overall, subjects judged the complex abstractthe one with the
nonsense mathematicsto be of higher quality.
Researchers are aware that they can advance their careers by writing in a complex way.
MIT students developed SCIgen, computer software to randomly select common but
complex words and apply grammar rules to produce documents that pass as research
papers on computer science. The title of one paper generated by the software was:
“Simulating Flip-flop Gates Using Peer-to-peer Methodologies.” At least 120 such
computer-generated papers were published in peer-reviewed scientific journals (Labbé
and Labbé, 2013; Lott, 2014).
Juster (1972, p. 23) states, “Few people would accept the naïve no-change model even if
it were clearly shown to be more accurate.” This supposition was supported by Hogarth’s
(2012) description of four key developments in forecasting in which senior academics
resisted overwhelming evidence that simple methods provide forecasts that are more
accurate than those from complex ones.
Clients might prefer forecasts that support their plans—another reason for the popularity
of complexity in forecasting. Developing complex methods that can be used to provide
forecasts that support a desired outcome is relatively easy.
5. Discussion
During our more than two years working on this special issue, we made repeated
requests for experimental evidence that complexity improves forecast accuracy under some
conditions. With the enormous efforts and expenditures on analytics and other complex big
data methods, one would expect some papers to provide evidence in favor of complexity in
forecasting. We have not been able to find such papers, despite our efforts to do so.
5.1. Summary of evidence from this review
To obtain a rough idea of the effects of complexity on ex ante forecast accuracy we
examined the studies described in this article to find estimates for the direction and size of
the effects. The assessments are crude because the definitions of simplicity vary across the
different studies. We do not, therefore, claim that our estimate of the effect of complexity
on forecast accuracy is definitive, nor do we claim that our review was comprehensive.
We hope that other researchers will expand on our work, and perhaps find forecasting
problems for which complexity produces forecasts that are substantially more accurate
than forecasts from sophisticatedly simple methods. Our judgments are provided at, so others can examine the effects of their own judgments as they
see fit.
In total we identify 32 papers—journal articles and book chapters—incorporating 97
formal comparisons of the accuracy of forecasts from complex methods with those from
simple—but not in all cases sophisticatedly simple—methods. Eighty-one percent of the
comparisons found that forecasts from simple methods were more accurate than, or
similarly accurate to, those from complex methods. Averaged across the 25 papers that
provide quantitative comparisons, the errors of forecasts from complex methods were 27
percent greater than the errors of forecasts from simple methods. The Table summarizes
Summary of evidence on accuracy of forecasts from complex vs. simple methods
--------- Number of Comparisons ---------
Method type
better or
increase vs
simple (%)
All method types
Weighted average*
*Weighted by total papers
5.2. Predicting unusual events
Simple evidence-based methods seem well equipped to deal with the problem of
predicting unusual events.!M2;!+J/5=6+<!N0:262=2462-<!O0.-/<!P+.;2=2462-<!Q24?024:2-<!
!!!!!)*+!037+J!5+.*27!is another simple approach that is well suited to forecasting unusual
events. Q8!/662>03?!@2;+1/-.+;-!.2!031647+!all variables that are known to be important in
a model, an index model is more likely to accurately predict an extreme event than is a
statistical model estimated from historical data on a subset of variables that does not
include all possible combinations of variable values.
5.3. Other evidence on simplicity versus complexity in forecasting
An alternative approach to assess the effects of simplicity in forecasting is to assess the
simplicity of evidence-based methods that have been shown to produce accurate forecasts.
The Forecasting Methods Selection Treeavailable online at
presents such forecasting methods in the form of a decision tree. The Tree is the product of
40 leading experts in various areas of forecasting from different disciplines, and 123
reviewers (Armstrong 2001), along with evidence cited on the
site since 2001.
None of the 22 methods in the Selection Tree is complex by the definition proposed in
this paper. In other words, the evidence-based methods that are recommended for use
because they have been shown to offer superior forecasting accuracy are all simple.
5.4. Evidence to date favors simplicity in forecasting
The evidence on comparative predictive validity along with the evidence related to the
effective methods listed in the Forecasting Methods Selection Tree constitute strong
arguments for starting simple when forecasting, and adding complexity only if needed. To
the best of the authors of this article’s knowledge, the need for complexity has not arisen.
Perhaps future research will identify benefits from complexity under some conditions. To
establish such a claim would, however, require that researchers test their complex methods
against sophisticatedly simple evidence-based methods, and publish their findings
regardless of the results.
Work on this JBR Special Issue on simplicity in forecasting began with the expectation
that simple forecasting would help to improve understanding, reduce mistakes, reveal bias,
and identify fraud. The authors expected that forecasts from simple methods would also
generally tend to be somewhat more accurate, but were concerned that the research
literature would not present a true picture of simplicity in forecasting. In particular,
researcher bias toward confirmation of their hypotheseswhether intended or notwould
likely produce an overabundance of studies finding in favor of complex methods.
Moreover, referee bias against simple methods likely has a damping effect on the number
of papers that find in favor of simple methods. The results, then, astonish the authors. The
results are consistent across the papers in finding in favor of simple methods, to the extent
that complex methods bring with them a forecast error penalty of about one-quarter.
The gains from simplicity identified here are consistent with the gains from following
the simple guidelines of the Golden Rule of Forecasting (Armstrong, Green, and Graefe,
this issue). In that article, violating a typical guideline increased error by about one-third,
and each additional violation would cause further losses in accuracy. The substantial gains
in accuracy that are possible from sophisticatedly simple forecasting are a tribute to a half-
century of research by the evidence-based forecasting community.
6. Summary and conclusions
The search for evidence for this introduction to the Special Issue ends with the
conclusion that forecasting procedures should always be simple enough for forecast users
to understand. Complexity beyond the sophisticatedly simple fails to improve accuracy in
all but 16 of the 97 comparisons in 32 papers that provide evidence. Complexity increases
forecast error by an average of 27 percent across the 25 papers with quantitative
comparisons. In addition to accuracy, simple methods can increase understanding, reduce
the likelihood of errors, and aid decision-makers.
Remarkably, no matter what type of forecasting method is used, complexity harms
accuracy. Complexity increases errors for forecasts from judgmental, extrapolative, and
causal methods by an average of more than 25 percent. Complexity when combining
forecasts increases errors by nearly 25 percent. Moreover, all of the 22 useful evidence-
based methods found by the forecasting principles project are simple.
Given the weight of evidence and the manifest advantages of simplicity, the advocates
of complexity in forecasting surely must be the ones to shoulder the burden of proving that
their methods and models will provide forecasts that are accurate relative to those from
sophisticatedly simple ones. They have so far failed to do so.
This introduction to the Special Issue describes how forecast users can evaluate the
simplicity of forecasting methods. A simplicity checklistwhich should take only minutes
to completeis available at to guide those evaluations. Obtaining
independent ratings of simplicity from several objective raters is desirable, but even a
single rating would alert the user to harmful complexity.
If you nevertheless use forecasts from complex methods to help you make decisions,
expect to be confused about how the forecasts were made and an accuracy penalty of more
than one-quarter. Forecast accuracy in many fields has failed to improve not because of a
lack of knowledge about how to forecast better, but due to a preference for complexity.
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... endfor (11) Rerr � RMSE(R − WT) 2 // Calculate the objective function (12) if Rerr < threshold (13) Break (14) Endif. (15) Endfor. ...
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Forecast combinations have flourished remarkably in the forecasting community and, in recent years, have become part of the mainstream of forecasting research and activities. Combining multiple forecasts produced from the single (target) series is now widely used to improve accuracy through the integration of information gleaned from different sources, thereby mitigating the risk of identifying a single "best" forecast. Combination schemes have evolved from simple combination methods without estimation, to sophisticated methods involving time-varying weights, nonlinear combinations, correlations among components, and cross-learning. They include combining point forecasts, and combining probabilistic forecasts. This paper provides an up-to-date review of the extensive literature on forecast combinations, together with reference to available open-source software implementations. We discuss the potential and limitations of various methods and highlight how these ideas have developed over time. Some important issues concerning the utility of forecast combinations are also surveyed. Finally, we conclude with current research gaps and potential insights for future research.
... While the complete parameterisation of a dynamic network model is itself challenging, high levels of model complexity do not necessarily guarantee high predictability (Figure 5.1). Indeed, there is no evidence that complex models are better than simple ones for forecasting system dynamics (Green and Armstrong 2015). As a result of the propagation of uncertainty, complex models often amplify prediction errors and result in prediction failures. ...
Until now, biological invasions have been conceptualised and studied mainly as a linear process: from introduction to establishment to spread. This volume charts a new course for the field, drawing on key developments in network ecology and complexity science. It defines an agenda for Invasion Science 2.0 by providing new framings and classification of research topics and by offering tentative solutions to vexing problems. In particular, it conceptualises a transformative ecosystem as an open adaptive network with critical transitions and turnover, with resident species heuristically learning and fine-tuning their niches and roles in a multiplayer eco-evolutionary game. It erects signposts pertaining to network interactions, structures, stability, dynamics, scaling, and invasibility. It is not a recipe book or a road map, but an atlas of possibilities: a 'hitchhiker's guide'.
We find that avatar design can reduce algorithm aversion, which is the tendency of decision makers to ignore advice received from an algorithm after the algorithm makes an error. When the facial features of an avatar exhibit high levels of competence, algorithm aversion can be reduced relative to no avatar or a less competent-looking avatar. Humanizing the financial advice from an algorithm with an avatar that promotes the perception of competence effectively reduces algorithm aversion and can enhance reliance on the financial advice of robo-advisors.
Purpose The purpose of this paper is to enlarge the exposure of the Theil–Sen (TS) methodology to the academic, analyst and practitioner communities using an earnings forecast setting. The study includes an appendix that describes the TS model in very basic terms and SAS code to assist readers in the implementation of the TS model. The study also presents an alternative approach to deflating or scaling variables. Design/methodology/approach Archival in nature using a combination of regression analysis and binomial tests. Findings The binomial test results support the hypothesis that the forecasting performance of the naïve no-change model is at least equal to or better than the ordinary least squares (OLS) model when earnings volatility is low. However, the results do not support the same hypothesis for the TS model nor do the results support the hypothesis that the OLS and TS models will outperform the naïve no-change model when cash flow volatility is high. Nevertheless, the study makes notable contributions to the literature, as the results indicate that the performance of the naïve model is at least as good as the OLS and TS models across 18 of the 20 binomial tests. Moreover, the results indicate that the performance of the TS model is always superior to the OLS model. Research limitations/implications The results are generalizable to US firms and may not extend to non-US firms. Practical implications The TS methodology is advantageous to OLS in that the results are robust to outlier observations, and there is no heteroscedasticity. Researchers will find this study to be useful given the use of a model (i.e. TS) which has to date received little attention, and the provision of the details for the mechanics of the model. A bonus for researchers is that the study includes SAS code for implementing the procedure. Social implications Awareness of alternative forecast methodologies could lead to improved forecasting results in certain contexts. The study also helps the financial community in general, as improved forecasting abilities are important for all capital market participants as they improve market efficiency. Originality/value Although a healthy literature exists for examining out-of-sample forecasts for earnings, the literature lacks an answer for a simple question before pursuing additional analyses: Are the results any better than those from a naive no-change forecast? The current study emphasizes the idea that the naïve no-change forecast is the most elementary model possible, and the researcher must first establish the superiority of a more complex model before conducting further analyses.
The M5 forecasting competition has provided strong empirical evidence that machine learning methods can outperform statistical methods: in essence, complex methods can be more accurate than simple ones. Regardless, this result challenges the flagship empirical result that led the forecasting discipline for the last four decades: keep methods sophisticatedly simple. Nevertheless, this was a first, and we can argue that this will not happen again. There has been a different winner in each forecasting competition. This inevitably raises the question: can a method win more than once (and should it be expected to)? Furthermore, we argue for the need to elaborate on the perks of competing methods, and what makes them winners?
We present a novel method for forecasting with limited information, that is for forecasting short time series. Our method is simple and intuitive; it relates to the most fundamental forecasting benchmark and is straightforward to implement. We present the technical details of the method and explain the nuances of how it works via two illustrative examples, with the use of employment‐related data. We find that our new method outperforms standard forecasting methods and thus offers considerable utility in applied management research. The implications of our findings suggest that forecasting short time series, of which one can find many examples in business and management, is viable and can be of considerable practical help for both research and practice – even when the information available to analysts and decision‐makers is limited.
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People often use analogies when forecasting, but in an unstructured manner. We propose a structured judgmental procedure whereby experts list analogies, rate similarity to the target, and match outcomes with possible target outcomes. An administrator would then derive a forecast from the information. When predicting decisions made in eight conflict situations, unaided experts’ forecasts were little better than chance at 32% accurate. In contrast, 46% of structured-analogies forecasts were accurate. Among experts who were able to think of two or more analogies and who had direct experience with their closest analogy, 60% of forecasts were accurate. Collaboration did not help. Key words: availability, case-based reasoning, comparison, decision, method.
Principles of Forecasting: A Handbook for Researchers and Practitioners summarizes knowledge from experts and from empirical studies. It provides guidelines that can be applied in fields such as economics, sociology, and psychology. It applies to problems such as those in finance (How much is this company worth?), marketing (Will a new product be successful?), personnel (How can we identify the best job candidates?), and production (What level of inventories should be kept?). The book is edited by Professor J. Scott Armstrong of the Wharton School, University of Pennsylvania. Contributions were written by 40 leading experts in forecasting, and the 30 chapters cover all types of forecasting methods. There are judgmental methods such as Delphi, role-playing, and intentions studies. Quantitative methods include econometric methods, expert systems, and extrapolation. Some methods, such as conjoint analysis, analogies, and rule-based forecasting, integrate quantitative and judgmental procedures. In each area, the authors identify what is known in the form of `if-then principles', and they summarize evidence on these principles. The project, developed over a four-year period, represents the first book to summarize all that is known about forecasting and to present it so that it can be used by researchers and practitioners. To ensure that the principles are correct, the authors reviewed one another's papers. In addition, external reviews were provided by more than 120 experts, some of whom reviewed many of the papers. The book includes the first comprehensive forecasting dictionary.
One of the most important commercial applications of forecasting can be found in the late stages of the new product development process for a new product, at which time managers seek to obtain accurate projections of market penetration for planning purposes. We review past work in this area and summarize much of it through ten principles. Several model characteristics, such as covariate effects (e.g., promotional measures) and capturing consumer heterogeneity are critical elements for a timely, accurate forecast; in contrast, other features such as a complex structural model and a “never triers” component are often detrimental to the model’s forecasting capabilities. We also make recommendations about certain implementation issues, such as estimation method (maximum likelihood is best) and the length of the calibration period (which is greatly dependent on the presence or absence of covariates). A set of practical implications for forecasters are identified, along with future research needs.