Spyros Makridakis

The M3-Competition: results, conclusions and implications

Abstract This paper describes the M3-Competition, the latest of the M-Competitions. It explains the reasons for conducting the competition and summarizes its results and conclusions. In addition, the paper compares such results/conclusions with those of the previous two M-Competitions as well as with those of other major empirical studies. Finally, the implications of these results and conclusions are considered, their consequences for both the theory and practice of forecasting are explored and directions for future research are contemplated.

The Combination of Forecasts

Aggregating information by combining forecasts from two or more forecasting methods is an alternative to using just a single method. In this paper we provide extensive empirical results showing that combined forecasts obtained through weighted averages can be quite accurate. Five procedures for estimating weights are investigated, and two appear to be superior to the others. These two procedures provide forecasts that are more accurate overall than forecasts from individual methods. Furthermore, they are superior to forecasts found from a simple unweighted average of the same methods.

The M2-competition: A real-time judgmentally based forecasting study

The purpose of the M2-Competition is to determine the post sample accuracy of various forecasting methods. It is an empirical study organized in such a way as to avoid the major criticism of the M-Competition that forecasters in real situations can use additional information to improve the predictive accuracy of quantitative methods. Such information might involve inside knowledge (e.g. a machine breakdown, a forthcoming strike in a major competitor, a steep price increase, etc.), be related to the expected state of the industry or economy that might affect the product(s) involved, or be the outcome of a careful study of the historical data and special care in procedure/methods employed while forecasting. The MZCompetition consisted of distributing 29 actual series (23 of these series came from four companies and six were of macro economic nature) to five forecasters. The data covered information including the September figures of the year involved. The objective was to make monthly forecasts covering 1.5 months starting from October and including December of the next year. A year later the forecasters were provided with the new data as they had become available and the process of predicting for 15 months ahead was repeated. In addition to being able to incorporate their predictions about the state of the economy and that of the industry the participating forecasters could ask for any

Generalising about univariate forecasting methods: further empirical evidence

Abstract This paper extends the empirical evidence on the forecasting accuracy of extrapolative methods. The robustness of the major conclusions of the M-Competition data is examined in the context of the telecommunications data of Fildes (1992) . The performance of Robust Trend, found to be a successful method for forecasting the telecommunications data by Fildes, is compared with that of other successful methods using the M-Competition data. Although it is established that the structure of the telecommunications data is more homogeneous than that of the M-Competition data, the major conclusions of the M-Competition continue to hold for this new data set. In addition, while the Robust Trend method is confirmed to be the best performing method for the telecommunications data, for the 1001 M-Competition series, this method is outperformed by methods such as Single or Damped Smoothing. The performance of smoothing methods depended on how the smoothing parameters are estimated. Optimisation at each time origin was more accurate than optimisation at the first time origin, which in turn is shown to be superior to arbitrary (literature based) fixed values. In contrast to the last point, a data based choice of fixed smoothing constants from a cross-sectional study of the time series was found to perform well.

Why combining works

Abstract The purpose of this paper is to explore the reasons why combining works, discuss the implications involved and propose guidelines for improving the field of forecasting by exploiting the reasons that contribute to the success of combining.

The art and science of forecasting An assessment and future directions

Abstract After several decades of important theoretical developments, practical experience gained through applications, and the findings of many empirical studies the field of forecasting is entering into a stage of maturity. The purpose of this paper is to assess its performance, evaluate its accomplishments, point out its shortcomings, propose directions for future research as well as ways of improving its usefulness and relevance. A major objective of this paper is to stimulate discussion. The author, being also editor of this journal, believes that the current debate going on within the field is necessary and useful. Problems facing the field must be identified and accepted before solutions can be found. Maturity can only come through some form of consensus among the researchers and practitioners in the field. Alternative opinions and proposals to those expressed in this paper are invited. Practitioners are particularly welcome to join the debate.

Factors affecting judgmental forecasts and confidence intervals

Eighteen time series differing in their trend (three categories), randomness (three categories), and presentation on a graph (two categories) were given to 350 MBA students in a laboratory experiment. Each student was asked to estimate judgmentahy a forecast and confidence interval. The results showed that when compared to the commonly used forecasting approach of simple regression, the judgmental forecasts differed significantly in their response to trend and presentation but not to randomness. The judgmental confidence intervals were very intluenced by trend but insufficiently influenced by randomness when compared to the regression estimates. o 1989 Academic PWSS. inc.

ARMA Models and the Box–Jenkins Methodology

The purpose of this paper is to apply the Box‐Jenkins methodology to ARIMA models and determine the reasons why in empirical tests it is found that the post-sample forecasting the accuracy of such models is generally worse than much simpler time series methods. The paper concludes that the major problem is the way of making the series stationary in its mean (i.e. the method of diAerencing) that has been proposed by Box and Jenkins. If alternative approaches are utilized to remove and extrapolate the trend in the data, ARMA models outperform the models selected through Box‐Jenkins methodology. In addition, it is shown that using ARMA models to seasonally adjusted data slightly improves post-sample accuracies while simplifying the use of ARMA models. It is also confirmed that transformations slightly improve post-sample forecasting accuracy, particularly for long forecasting horizons. Finally, it is demonstrated that AR(1), AR(2) and ARMA(1,1) models can produce more accurate post-sample forecasts than those found through the application of Box‐ Jenkins methodology. #1997 by John Wiley & Sons, Ltd.

Forecasting: its role and value for planning and strategy

Long-term predictions are indispensable for planning and strategy. Yet little is known about their value, their limitations or the most appropriate way of making and using them. This paper examines these issues and proposes two approaches to long-term forecasting while illustrating their use to planning and strategy. The first approach consists of identifying and extrapolating critical long-term trends while assessing their impact on society and firms. The second approach studies the analogy of the industrial and information revolutions and the specific consequences of the industrial revolutions five most important inventions in terms of the consequences of similar ones of the information revolution. The paper concludes by advocating that much needs to be done to integrate forecasting, on the one hand, and long-term planning and strategy, on the other. The purpose of such integration is to increase the ability of organizations to anticipate important, forthcoming changes, and their consequences, and successfully adapt themselves to these changes as well as the opportunities and dangers associated with them.

Confidence intervals: An empirical investigation of the series in the M-competition

Abstract This paper empirically evaluates the uncertainty of forecasts. It does so using the 1001 series of the M-Competition. The study indicates that although, in model fitting the percentage of observations outside the confidence intervals is close to that postulated theoretically, this is not true for forecasting. In the latter case the percentage of observations outside the confidence intervals is much higher than that postulated theoretically. This is so for the great majority of series, forecasting horizonts, and methods. In addition to evaluating the extent of uncertainty, we provide tables to help users to construct more realistic confidence intervals for their forecasts.