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A Framework for the Combination of Forecasts

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Abstract

A framework for the systematic study of the combination of sales and market forecasts is proposed based on the types of forecasts to be combined and the methods used to combine them. A detailed survey of the literature is given in terms of the developed framework and general conclusions about the combination of forecasts area are developed. Some future needs for research are also discussed.

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... Para fazer uso da combinação e poder capturar os fatores que afetam as previsões, é preciso saber quais técnicas utilizar e como combiná-las. Flores & White (1988) propõem uma estrutura que visa atender a esses fi ns, estabelecendo, respectivamente, duas dimensões: (i) seleção das técnicas de previsão-base e (ii) seleção do método de combinação. ...
... As previsões-base são classifi cadas, conforme Flores & White (1988), em três categorias: objetivas, subjetivas ou através da utilização de ambas (objetivas e subjetivas). A categoria objetiva engloba regressão, modelos Box-Jenkins e outros procedimentos com base matemática. ...
... De acordo com Flores & White (1988), os primeiros esforços foram feitos para combinar objetivamente previsões com base objetiva, tais como as propostas apresentadas anteriormente. Ainda segundo os autores, tem-se a combinação objetiva utilizando previsões com base subjetiva, sendo que a maioria dos estudos tem enfoque bayesiano. ...
Article
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Realizar previsões de demanda é uma atividade importante na empresa, entretanto, usar uma única técnica para obtê-las pode não ser suficiente para incorporar todo o conhecimento associado ao ambiente de previsão. As formas de integração de previsões incorporam várias técnicas e têm mostrado potencial para reduzir o erro de previsão. Este trabalho apresenta uma modelagem que está estruturada utilizando: combinação de previsões e ajuste baseado na opinião. Os elementos incluídos na modelagem são: dados históricos; econômicos; e de especialistas. Após obter-se a previsão combinada, aplica-se um ajuste para obter a previsão final. O modelo proposto é ilustrado através de uma aplicação.
... Para fazer uso da combinação e poder capturar os fatores que afetam as previsões, é preciso saber quais técnicas utilizar e como combiná-las. Flores & White (1988) propõem uma estrutura que visa atender a esses fi ns, estabelecendo, respectivamente, duas dimensões: (i) seleção das técnicas de previsão-base e (ii) seleção do método de combinação. ...
... As previsões-base são classifi cadas, conforme Flores & White (1988), em três categorias: objetivas, subjetivas ou através da utilização de ambas (objetivas e subjetivas). A categoria objetiva engloba regressão, modelos Box-Jenkins e outros procedimentos com base matemática. ...
... De acordo com Flores & White (1988), os primeiros esforços foram feitos para combinar objetivamente previsões com base objetiva, tais como as propostas apresentadas anteriormente. Ainda segundo os autores, tem-se a combinação objetiva utilizando previsões com base subjetiva, sendo que a maioria dos estudos tem enfoque bayesiano. ...
Article
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Demand forecasting is an important task in the companies, however the use of a single technique to produce forecasts might not be enough to gather all the knowledge associated with the forecast environment. The way to integrate forecasts incorporates various techniques and has show potential to reduce forecast error. This study presents a model that relies on the use of two means of integration: forecast combination and judgmental adjustment. The elements covered by the presented model are: historic data, economic data, and the opinion of experts. After obtaining the combined forecast, an adjustment based on the experts' opinion is applied to attain the final forecast. The model proposed is described in details and illustrated through a practical application.
... Forecasting methods can be categorized into two broad categories: (1) those based primarily on judgment (e.g., Mentzer and Kahn 1995;Sanders and Manrodt 1994) and (2) those based on statistical sources. Research on forecast combination has focused on the delineation of normatively appropriate ways to combine forecasts and has acknowledged that more work is needed to describe the actual integration process that decision makers use (Clemen 1989;Flores and White 1988). The goal of this article is to describe this process and highlight the potential deviation of the outcome from a normative benchmark. ...
... For example, if the two forecasts are not as discrepant as the forecasts we have used, it is possible that extraneous range information will not be evoked and used. Given the well-acknowledged importance of forecasting in managerial decision making and the lack of research on how decision makers actually combine forecasts (Clemen 1989;Flores and White 1988), additional work is needed that addresses these issues. ...
Article
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The authors hypothesize that when managers integrate two projections to form a sales estimate, they evoke and use a sales range to judge inap-propriately the plausibility of each projection. This judged plausibility, as well as the "margin of error" (based on the market research company's typical accuracy), is used to assign weights to each projection. Five experiments find strong evidence for this process and demonstrate a resulting bias.
... The utilization of forecast combinations is justified by the facts that: (i) there is no perfect forecasting technique, since there is no way to acquire the reality exactly as it is; (ii) it's not known if a forecasting technique will always present a better performance than other techniques in all periods and forecast horizon intervals using the whole series of data (Flores & White, 1988 According to Flores and White (1988), in order to use a combination of forecasts, the selection of the base forecast techniques is necessary to determine which forecasts to include in the combination. One must then choose the combination methods, which is how the individual techniques will be combined. ...
... The utilization of forecast combinations is justified by the facts that: (i) there is no perfect forecasting technique, since there is no way to acquire the reality exactly as it is; (ii) it's not known if a forecasting technique will always present a better performance than other techniques in all periods and forecast horizon intervals using the whole series of data (Flores & White, 1988 According to Flores and White (1988), in order to use a combination of forecasts, the selection of the base forecast techniques is necessary to determine which forecasts to include in the combination. One must then choose the combination methods, which is how the individual techniques will be combined. ...
Article
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A systematic approach for evaluating the performance of individual techniques and their combinations to forecast urban water demand is proposed and organized into four phases in this work. It uses three forecasting techniques: exponential smoothing (ES), seasonal autoregressive integrated moving average (SARIMA) and artificial neural networks (ANN) models. 14 combinations of forecasts are evaluated with the goal of improving the estimation accuracy. This systematic approach was applied to monthly data over an interval from 2000 until 2011 (with a validation set of 12 months). Data from 10 cities in the state of Paraná, Brazil were evaluated. In choosing the best model for each city, the combinations are highlighted. According to a Mean Absolute Percentage Error (MAPE) criterion, results indicate that the choice of the most accurate model of ES or SARIMA produces the best forecasting global performance, which had the smallest standard deviation (0.667%) and a MAPE of 3.297%.
... background Practically every important decision involves integration of information 1 from multiple sources. Thus, it is not surprising that there is a voluminous literature that addresses various facets of the information aggregation process (see Armstrong, 2001;Clemen, 1989;Ferrel, 1985;Flores & White, 1988;Hogarth, 1977;Rantilla & Budescu, 1999, for partial reviews of this body of work). Interest in the aggregation problem cuts across disciplinary and paradigmatic boundaries, although it takes different forms and focuses on distinct questions in the various cases (Budescu, 2001;Rantilla & Budescu, 1999). ...
Article
To the memory of my friend and colleague, Janet A. Sniezek (1951–2003) This chapter summarizes research related to several interrelated questions regarding the process by which single decision makers (DMs) aggregate probabilistic information regarding a certain event from several, possibly asymmetric, advisors who rely on multiple and, possibly overlapping and correlated, sources of information. In particular I seek to understand and characterize (a) the nature of the aggregation rules used by DMs and (b) the factors that affect the DMs’ confidence in the final aggregate. The chapter starts with a short literature overview whose main goal is to set the stage by placing this work within the broad area of information aggregation. Next I present a descriptive model of confidence in information integration that is based on two principles: (a) People combine multiple sources of information by applying simple averaging rules; and (b) the DM’s level of confidence in the aggregate is a monotonically decreasing function of its perceived variance. Some of the model’s predictions regarding the structural and natural factors that affect the DM’s confidence are discussed and tested with empirical data from four experiments (Budescu & Rantilla, 2000; Budescu et al., 2003). The results document the relation between the DM’s confidence and the amount of information underlying the forecasts (number of advisors and cues), the advisors’ accuracy, and the distribution of cues over judges with special attention to the level of interjudge overlap in information.
... Estas previsões são, então, combinadas, gerando a previsão final (WEBBY & O'CONNOR, 1996). Flores & White (1988) propõem uma estrutura para combinação de previsões que estabelece duas dimensões: (i) seleção das técnicas de previsão-base, onde define-se quais previsões incluir na combinação, isto é, selecionam-se as técnicas que irão participar da combinação; e (ii) seleção do método de combinação, onde define-se a forma de combinação das técnicas. Segundo Clemen (1989), métodos têm sido desenvolvidos para encontrar a melhor combinação de previsões e o resultado tem sido unânime: combinar previsões conduz ao aumento de acurácia da previsão (combinada) em relação a qualquer previsão individual. ...
Article
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Este artigo apresenta uma metodologia para previsão de demanda por energia elétrica nas conexões da rede de distribuição de concessionárias. A sistemática de contratação de energia, por parte das concessionárias, junto às empresas transmissoras, exige a realização de previsões abrangendo extensas áreas de concessão, diversos segmentos econômicos e horários distintos. Para tanto, propõe-se a utilização de uma sistemática que combina previsões matemáticas, obtidas através de um modelo de decomposição robusto a ocorrência de eventos especiais, a opiniões de especialistas. A metodologia proposta é ilustrada através de um estudo de caso em uma distribuidora de energia elétrica da região sul do país.
... The idea to combine foresight methods has a long history. In 1988, Flores and White proposed to structure literature on combined forecasting methodologies along two tracks: (1) "selection of the base forecasts" which determines which forecasts to include-qualitative, quantitative, or both-, and (2) the "selection of the method of combination" which is concerned with the approach to combine them, i.e., systematically, or in an intuitive way [63]. ...
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To ensure long-term competitiveness, companies need to develop the ability to explore, plan, and develop new business fields. A suitable approach faces multiple challenges because it needs to (1) integrate multiple perspectives, (2) ensure a high level of participation of the major stakeholders and decision-makers, (3) function despite a high level of uncertainty, and (4) take into account interdependencies between the influencing factors. In this paper, we present an integrated approach that combines multiple strategic-foresight methods in a synergetic way. It was applied in an inter-organizational business field exploration project in the telecommunications industry.
... Ou seja, até aqui são necessários p+1 estágios de ajustes. Por fim, as previsões híbridas linearmente combinadas para as componentes wavelet de aproximação e de detalhe são combinadas, também de forma linear, tal como em (10). ŷ CL,wave,t : = [(ρ V m 0 (ϕ) × ŷ V m 0 (ϕ),CL,t ) + ∑ (ρ W m (ω) × ŷ W m (ω),CL,t ) m 0 +(p−1) m=m 0 ] + β CL,wave (10) Onde: ŷ V m 0 (ϕ),CL,t é a previsão linearmente para y V m 0 (ϕ),t ; ŷ W m (ω),CL,t é a previsão linearmente para y W m (ω),t ; ρ V m 0 (ϕ) é peso adaptativos associado à previsão ŷ V m 0 (ϕ),CL,t ; ρ W m (ω) é peso adaptativos associado à previsão ŷ W m (ω),CL,t ; β CL,wave é a constante adaptativa aditiva; e ŷ CL,wave,t é a previsão linearmente combinada para o ponto y t . ...
Conference Paper
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In this paper, we put forward a hybrid methodology for combining forecasts to (stochastic) time series referred to as Wavelet Linear Combination (WLC) SARIMA-RNA with Multiple Stages. Firstly, the wavelet decomposition of level p is performed, generating (approximations of the) p+1 wavelet components (WCs). Then, the WCs are individually modeled by means of a Box and Jenkins’ model and an artificial neural network - in order to capture, respectively, plausible linear and non-linear structures of autodependence - for, then, being linearly combined, providing hybrid forecasts for each one. Finally, all of them are linearly combined by the WLC of forecasts (to be defined). For evaluating it, we used the Box and Jenkins’ (BJ) models, artificial neural networks (ANN), and its traditional Linear Combination (LC1) of forecasts; and ANN integrated with the wavelet decomposition (ANNWAVELET), BJ model integrated with the wavelet decomposition (BJ-WAVELET), and its conventional Linear Combination (LC2) of forecasts. All predictive methods applied to the monthly time series of average flow of tributaries of the Itaipu Dam dam, located in Foz do Iguacu, Brazil. In all analysis, the proposed hybrid methodology has provided higher predictive performance than the other ones.
... The research on aggregation covers an extensive range of substantive areas, such as weather forecasting (e.g., Clemen & Murphy, 1986;Clemen & Winkler, 1987), business (e.g., Ashton, 1986;Ashton & Ashton, 1985;Fischer & Harvey, 1999), and assorted prediction tasks (Fischer, 1981;Fischer & Harvey, 1999;Harvey, Harries, & Fischer, 2000;Hogarth, 1989). A complete review of this research is beyond the scope of this article, but the reader can consult several excellent literature reviews (e.g., Armstrong, 2001;Clemen, 1989;Ferrell, 1985;Flores & White, 1988). ...
Article
We study the process by which decision makers (DMs) aggregate probabilistic opinions from multiple, correlated sources with a special emphasis on the determinants of the DM's confidence, which is a predictor of the DM's willingness to accept the implications of the aggregation process. Our model assumes that (a) DM combines the advisors' opinions by weighting them according to the amount of information underlying them, and (b) the DM's confidence increases as a function of a variety of factors that reduce the variance of the aggregate. We report results of three studies that manipulate the predictive validity of the cues and their inter-correlations. Most of the models' predictions are supported but, contrary to the model's prediction, the DMs' confidence is not sensitive to the inter-cue correlation. The best predictors of the DMs' confidence are the perceived predictability of the event, the level of agreement among the advisors, and the advisors' self-reports of confidence. This pattern of results is explained by the ‘system neglect’ hypothesis. Copyright © 2006 John Wiley & Sons, Ltd.
... GEPROS. Gestão da Produção, Operações e Sistemas, Bauru, Ano 11, nº 1, jan-mar/2016, p. 79-95 Flores & White (1988), apud in Albino (2009), destacam dois aspectos básicos na combinação de previsões: (I) seleção das previsões a serem combinadas; e (II) escolha do método de combinação. As previsões a serem combinadas (obtidas por métodos individuais) podem ser classificadas em duas categorias: objetivas e subjetivas. ...
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This paper proposes a linear combination of forecasts obtained from three forecasting methods (namely, ARIMA, Exponential Smoothing and Artificial Neural Networks) whose adaptive weights are determined via a multi-objective non-linear programming problem, which seeks to minimize, simultaneously, the statistics: MAE, MAPE and MSE. The results achieved by the proposed combination are compared with the traditional approach of linear combinations of forecasts, where the optimum adaptive weights are determined only by minimizing the MSE; with the combination method by arithmetic mean; and with individual methods
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We investigate the case of a Decision Maker (DM) who obtains probabilistic forecasts regarding the occurrence of a target event from J distinct, asymmetric advisors. In this context, asymmetry is induced by manipulating: (1) amount of information (number of diagnostic cues) available to each advisor and (2) quality (accuracy) of advisors’ previous forecasts. Empirical results from two experiments indicate that the DM’s final estimate can be described as a weighted average of advisor forecasts, where the weights are sensitive to both sources of asymmetry. This work extends the model derived by Budescu and Rantilla (2000) for the DMs confidence in the aggregate to accommodate advisor asymmetry. As in the symmetric case, the DM’s confidence in the weighted average of the forecasts is a function of the number of judges, the total number of cues, the (inferred) inter-judge correlation, and the level of inter-judge overlap in information. The extended model predicts that confidence increases as a function of asymmetry among judges. Empirical results support the main (ordinal) predictions of the model, including the predicted effect of inter-judge asymmetry.
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Thesis
Firms are facing an increasingly complex environment and highly complex product and service landscapes that often require multiple organizations to collaborate for innovation and offerings. Research in this dissertation was based on the expectation that corporate foresight activities will increasingly be embedded in interorganizational settings and a) can draw on such settings for the benefit of themselves and b) may contribute to shared visions, trust building and planning in these network organizations. The goal of this dissertation is to contribute to the corporate foresight research field by investigating capabilities, practices, and challenges particularly in the context of interorganizational settings and networked organizations informed by the theoretical perspectives of the relational view and dynamic capabilities. The EIT Digital is a central case of this dissertation, supplemented with insights from three additional cases. Research draws on the rich theoretical understanding of the resource-based view, dynamic capabilities, and particularly the relational view to further the discussion in the field of corporate foresight—defined as foresight in organizations in contrast to foresight with a macro-economical perspective—towards a relational understanding. Further, Rohrbeck’s Maturity Model for the Future Orientation of Firms is used as conceptual frame for corporate foresight in interorganizational settings. The analyses—available as four individual publications complemented by on additional chapter—are designed as exploratory case studies based on multiple data sources including an interview series with 49 persons, two surveys (N=54, n=20), three supplementary interviews, access to key documents and presentations, and observation through participation in meetings and activities of the EIT Digital. This research setting allowed contributing to corporate foresight research and practice by 1) integrating relational constructs primarily drawn from the relational view and dynamic capabilities research into the corporate foresight research stream, 2) exploring and understanding capabilities that are required for corporate foresight in interorganizational and networked organizations, 3) discussing and extending the Maturity Model for network organizations, and 4) to support individual organizations to tie their foresight systems effectively to networked foresight systems.
Chapter
This paper develops a general indirect deterministic causal model (IDC model) for durable equipment. After the general model is introduced, an application is presented which models the sales for underground piping systems in the Petroleum Marketing Industry. It will be shown that the forecast of the IDC model leads to the correct investment decision. Also, the forecast of the IDC model will be compared to other time series forecasting methods (exponential smoothing and regression against time) for accuracy, information content, conditional efficiency, and effectiveness.
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Before 1960, little empirical research was done on forecasting methods. Since then, the literature has grown rapidly, especially in the area of judgmental forecasting. This research supports and adds to the forecasting guidelines proposed before 1960, such as the value of combining forecasts. New findings have led to significant gains in our ability to forecast and to help people to use forecasts. What have we reamed about forecasting over the past quarter century? Does recent research provide guidance for making more accurate forecasts, obtaining better assessments of uncertainty, or gaining acceptance of our forecasts?
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In an empirical study of sales forecasts, management judgment forecasts are compared with systematic forecasts (based on the Box-Jenkins ARIMA method). A composite sales forecasting model is developed which incorporates information from these different sources. In most cases forecast improvement apparently can be realized by combining multiple forecast inputs into a composite model. The concept of conditional efficiency then is introduced to evaluate the strength of an individual forecast input to the composite forecast. Upon finding the management judgment forecasts to be conditionally efficient on the basis of the composite model standard, the authors examine the management judgment forecasting task and environment in terms of the conditions which facilitate accurate management judgment predictions.
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A number of procedures for forecasting a time series from its own current and past values are surveyed. Forecasting performances of three methods--Box-Jenkins, Holt-Winters and stepwise autoregression--are compared over a large sample of economic time series. The possibility of combining individual forecasts in the production of an overall forecast is explored, and we present empirical results which indicate that such a procedure can frequently be profitable.
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When a panel of experts is assembled to make predictions about some aspect of the future, they invariably disagree. The possible strategies for dealing with such disagreement include (1) taking the statistical average of the individual forecasts, (2) face-to-face discussion until consensus is achieved, (3) the Delphi procedure, and (4) the Estimate-Talk-Estimate procedure proposed by D. H. Gustafson, R. K. Shukla, A. Delbecq, and G. W. Walster (Organizational Behavior and Performance, 1973). This paper does two things. First, it very briefly reviews the literature relevant to opinion aggregation when forecasts are expressed as subjective probability distributions. Second, it describes an experimental comparison of the four procedures listed above using a subjective probability forecasting task. Together, the review and the experiment lead to two conclusions. First, subjective probability forecasts can be substantially improved by aggregating the opinions of a group of experts rather than relying on a single expert. Second, from a practical standpoint, there is no evidence to suggest that the method used to aggregate opinions will have a substantial impact on the quality of the resulting forecast.
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The paper reports results of an experiment conducted to evaluate subjective versus objective combination of forecasts. The subjects were undergraduate students at Texas A&M. The students forecasted two different types of time series. The results found show that the subjective combination of forecasts improves their accuracy as compared with individual efforts. Four ex-ante weighting methods were also used to combine the forecasts. They all improve the accuracy of the forecasts. The best results, though, were from the subjective combination of forecasts.
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This study develops a general Bayesian approach to the problem of combining forecasts. This approach leads to the results of Bates and Granger in certain special cases and to a geometric averaging formula in other special cases.
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This paper examines some of the theoretical implications of combining forecasts using a minimum variance criterion. In particular, the derivation of the exact expression for the minimum variance weight vector is provided, together with a proof that the error variance of the composite forecast is no greater than that of any of the component forecasts. A detailed examination is made of the probability distributions of the weight estimators, and an explanation is given for the occurrence of negative weights.
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Forecasts may be combined using a minimum variance criterion to yield a composite forecast of smaller error variance than any of the components. This paper considers the sampling distributions of the weights to be attached to the components and of the error variance of the combined forecast. Confidence limits are derived for the estimates of the weights and of the variance of a composite forecast with two components. The theoretical analysis reveals that, in practice, it is doubtful whether combined forecasts offer much improvement because of the unreliability of the weight estimates.
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Many decision-theorists and forecasters have advocated the use of a linear combination of forecasts for decision-making purposes. However, there have been two separate themes. One has looked at providing linear weights which minimise the forecast error variance. The other has utilised the posterior probabilities derived from the conventional Bayesian model discrimination procedure. This paper has attempted to identify some practical circumstances in which one of these two approaches becomes the more appropriate.
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This paper is concerned with expanding the decision support capabilities of computerized forecasting systems. The expansion allows for the systematic combination of multiple forecasts and the explicit consideration of multiple objectives in the forecast selection process. The methodology used is multiple objective linear programming. Selecting an individual forecast based upon a single objective may not make the best use of available information for a variety of reasons. Combined forecasts may provide a better fit with respect to a single objective than any individual forecast. Even if an individual forecast does provide a good fit with respect to a single objective, a combined forecast may provide a better fit with respect to multiple objectives. An example is used to illustrate the expanded decision support system, its outputs and their properties.
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In the last few decades many methods have become available for forecasting. As always, when alternatives exist, choices need to be made so that an appropriate forecasting method can be selected and used for the specific situation being considered. This paper reports the results of a forecasting competition that provides information to facilitate such choice. Seven experts in each of the 24 methods forecasted up to 1001 series for six up to eighteen time horizons. The results of the competition are presented in this paper whose purpose is to provide empirical evidence about differences found to exist among the various extrapolative (time series) methods used in the competition.
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It is well known that a linear combination of forecasts can outperform individual forecasts. The common practice, however, is to obtain a weighted average of forecasts, with the weights adding up to unity. This paper considers three alternative approaches to obtaining linear combinations. It is shown that the best method is to add a constant term and not to constrain the weights to add to unity. These methods are tested with data on forecasts of quarterly hog prices, both within and out of sample. It is demonstrated that the optimum method proposed here is superior to the common practice of letting the weights add up to one.
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In this study, the author provides a brief and concise summary of empirical investigations pertaining to forecasting with special reference to the accuracy of different forecasting techniques. The study mainly focuses on comparisons of the accuracy of these techniques. The comparisons cover both quantitative and qualitative methods. In addition the summary includes studies seeking to test or improve accuracy by combining forecasting techniques.
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The weights used in the combination of forecasts are shown to be very unstable. They are generally so unstable that the combined forecasts often do not perform better than some of the individual forecasts or a simple average of the forecasts in practice. The instability is found from a series of Monte Carlo experiments as well as from the nominal GNP forecasts from four well-known macro forecasters. The Monte Carlo experiments also show that when the underlying models are known, a composite forecast from a composite model is generally more accurate than the combination of the individual forecasts. A simple average is shown to be the best technique to use in practice, because the weights in the combination are so unstable.
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Judgement based forecasts are widely used in practice either alone or in conjunction with computer prepared forecasts. This study empirically examines the improvement in accuracy which can be gained from combining judgemental forecasts, either with other judgemental or with quantitatively derived forecasts. Two judgemental forecasting approaches are used by each of two different groups in a laboratory setting to give four sets of judgemental forecasts for the 68 monthly time series of the M-competition. These are combined either with each other or with forecasts from deseasonalised single exponential smoothing. Combined forecasts are found to be more accurate than single forecasts with the greatest benefit realised at short forecast horizons and for easier (as opposed to harder) forecast series. Averaging was observed to be a far better way of combining judgemental forecasts than a judgemental, nonsystematic combination.
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The impact on forecast accuracy of aggregating the subjective forecasts of up to 13 individuals was examined for five forecast weighting methods---equal weighting, two ex post methods that took advantage of prior information about the individuals' relative accuracy, and two ex ante methods based on objective and subjective assessments of relative accuracy. The individuals were executives, managers and sales personnel employed by Time. Inc., and the variable forecasted was the number of advertising pages sold annually by Time magazine over a 14-year period. The results show that both the average forecast error and the variance of the error decrease as additional individuals' forecasts are included in the aggregate. Only two to five individuals' forecasts must be included to achieve much of the total improvement available from combining all 13 forecasts. Three of the differential weighting methods produced more accurate forecasts than equal weighting, but the magnitude of the improvement was small. Implications for realistic forecasting situations are discussed, as are conditions under which the use of aggregates seems attractive.
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This paper is about the motivation, methodology, and evaluation of combining the forecasts from two or more different models in a "combined" forecast. Granger and Newbold (Granger, C., P. Newbold. 1977. Forecasting Economic Time Series. Academic Press, New York.) have presented this method as one whereby an "optimal" forecast can be obtained. Makridakis and Winkler (1966) and Winkler and Makridakis (Winkler, R., S. Makridakis. 1983. The combination of forecasts: some empirical results. J. Roy. Statist. Soc., Ser. A 146 150--157.) have presented results to support this claim and Mahmoud (Mahmoud, Essam. 1984. Accuracy in forecasting: a survey. J. Forecasting 3 139--159.) has reviewed over 20 articles all claiming that combined forecasts out perform single model forecasts. This paper extends this topic in a number of directions. First a section on motivation provides additional reasons for combining forecasts. Combination problems are then discussed in §2, observations and evaluations of the problem presented are discussed in §3 and concluding remarks are contained in §4.
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Most time series methods assume that any trend will continue unabated, regardless of the forecast lead time. But recent empirical findings suggest that forecast accuracy can be improved by either damping or ignoring altogether trends which have a low probability of persistence. This paper develops an exponential smoothing model designed to damp erratic trends. The model is tested using the sample of 1,001 time series first analyzed by Makridakis et al. Compared to smoothing models based on a linear trend, the model improves forecast accuracy, particularly at long leadtimes. The model also compares favorably to sophisticated time series models noted for good long-range performance, such as those of Lewandowski and Parzen.
Article
Presented is a new application in urban economic forecasting. This method actively utilizes external information for household population forecasts. The purpose is to develop a more satisfying procedure as part of the management decision taking system. In the Portland Standard Metropolitan Statistical Area (SMSA), both time series and cross-sectional data are exploited. A transfer function-noise model is developed relating national output to SMSA employment. Household population for the SMSA is forecast utilizing the same statistical technique via a job opportunities/migration hypothesis. Forecasts are allocated to planning divisions within the SMSA by univariate stochastic models. However, these forecasts are adjusted after consideration of several land use indicators. The forecast standard errors are utilized and a hierarchical weighting scheme of the land-use indicators is developed within an allocation framework. Qualitative and quantitative information is merged to provide a more complete analysis and efficient estimates of the allocation weights.
Article
In seeking an efficient combination of forecasts which minimises the forecast error variance, many methods have been suggested. Through analysis, simulation and case studies, this paper seeks to develop insights into the statistical circumstances which influence the relative accuracy of six of these methods. The six methods chosen have all been advocated in various publications and consist of ‘equal weighting’ (i.e., pooled average), ‘optimal’ (i.e., error variance minimising), ‘optimal with independence assumption’ (i.e., error variance minimising assuming zero correlation between individual forecast errors) and three variations on the formulation of a Bayesian combination based upon posterior probabilities. The statistical circumstances reflected varying conditions of relative forecast errors, error correlations and outliers.
Article
Typescript. Thesis--University of Iowa, 1978. Bibliography: leaves 124-127.
Article
Thesis (Ph. D.)--State University of New York at Buffalo, 1982. Includes bibliographical references (leaves 336-370). Photocopy of typescript.
Article
Bayesian methodology is suggested as a valid approach to the combination of forecasts and a simple subjectivist procedure is presented. It is shown how subjective probabilities can be meaningfully assigned over a set of forecasting models and updated, according to a Bayesian process, when the forecast realizations become known.
Article
This paper records a personal view of the wide range of problems, philosophical and pragmatic, currently afflicting 'business forecasting'. It is based on several years experience in both forecasting methodology development and direct project work with decision makers. The paper is not intended as a review of the current consensus, academic or otherwise but to engage in 'constructive criticism'. In doing so the author has attempted to keep to the desired structure of 'decision makers perception', 'methodology criticised' and 'development suggestions' but the nature of the problem demands a more interactive approach which has resulted in fuzzy sets rather than distinct clusters of topics.
Article
Often decision makers have several forecasts of an uncertain and operationally relevant random variable. A rich literature now exists which argues that in this situation the decision maker should consider forming a forecast as a weighted average of each of the individual forecasts. In this paper, composite forecasting is discussed in a Bayesian context. The ability of the user to control the impact of the data on his composite weights is illustrated by an example using expert opinion forecasts of US hog prices.
Article
This paper reports on a comprehensive study of the distributions of summary measures of error for a large collection of quarterly multiperiod predictions of six variables representing inflation, real qrowth, unemployment,and percentage changes in nominal GNP and two of its more volatile components.The data come from surveys conducted since 1968 by the National Bureau of Economic Research and the American Statistical Association and cover more than 70 individuals professionally engaged in forecasting the course of the U. S.economy (mostly economists, analysts, and executives from the world of corporate business and finance). There is considerable differentiation among these forecasts, across the individuals, variables, and predictive horizons covered. Combining corresponding predictions from different sources can result insignificant gains; thus the group mean forecasts are on the average over timemore accurate than most of the corresponding sets of individual forecasts. But there is also a moderate deqree of consistency in the relative performance of a sufficient number of the survey members, as evidenced in positive rank correlations among ratios of the individual to group root mean square errors.
Article
This study analyzes the form, stability, and accuracy of Box-Jenkins forecasting models developed for 27 sales series. The order of autoregressive, differencing, and moving average factors is shown for each complete model along with “goodness of fit” criteria. Forecasting models are then presented for a reduced data set and accuracy is compared with seasonally adjusted linear regressions. The results suggest that Box-Jenkins models are often unstable, “goodness of fit” criteria are a poor guide to the best forecasting models, log transforms do not improve accuracy, and Box-Jenkins forecasts are usually (but not always) better than projections made with linear regression techniques.
Article
We present a general procedure for aggregating expert forecasts which exploits regularities in the structure of information within the forecaster population. Specific information structures lead to aggregation methods which adjust for additive bias, differences in individual accuracy, and correlation among forecasts. As an application, we construct composite predictions of the weekly change in the money supply from forecasts made by twenty major securities dealers, for which high positive correlation is found to be a significant characteristic. Due to instability in the information structure, our methods cannot improve on the accuracy of a simple average in this case. However, they do capture information about the correlation among money supply forecasts which is not fully impounded in short‐term interest rates. Forecasts from our models accurately predict the direction of price changes for Treasury bills and Treasury bill futures after a money supply announcement.
Combining Economic Forecasts
  • R Clemen
  • R Winkler
Developing Sales Forecasting - Master Scheduling Software
  • F J Chunglo
Comments to S. Armstrong paperThe Ombudsman: Research on Forecasting: A Quarter-Century Review, 1960-1984
  • E Gardner
Guesswork and Statistics in Sales Forecasting
  • J Gold
Econometric Models and Economic Forecasts
  • R Pindyck
  • D Rubinfeld
The Combination of Forecasts."
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  • C W J Granger
Technical Analysis Still Beats Econometries
  • S Goodman