A note on a comparison of exponential smoothing methods for forecasting seasonal series

doi:10.1016/0169-2070(89)90068-X

International Journal of Forecasting

Volume 5, Issue 1, 1989, Pages 111-116

https://doi.org/10.1016/0169-2070(89)90068-X Get rights and content

Abstract

Additive seasonal models and multiplicative seasonal models can be forecast using general exponential smoothing and Winters' methods. The two forecasting methods were compared using 47 of the 1001 time series which were used in the M-competition. Values of the optimal smoothing constants found when fitting the models are shown. Although Winters' models always resulted in a better squared error fit, these models gave a better forecast in only 55% of the series.

References (10)

Sonia M. Bartolomei
A comparison of exponential smoothing methods for forecasting seasonal series
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E.S. Gardner
Exponential smoothing: the state of the art
Journal of Forecasting
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E.S. Gardner et al.
Forecasting trends in time series
Management Science
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S. Makridakis et al.
The accuracy of extrapolation (time series) methods; results of a forecasting competition
Journal of Forecasting
(1982)

There are more references available in the full text version of this article.

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Assessment of wastewater treatment facility compliance with decreasing ammonia discharge limits using a regression tree model
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Out-of-sample validation of the regression tree models is performed using four years of effluent ammonia and flow data from an operating wastewater treatment facility in Colorado. Out-of-sample evaluation of forecasting accuracy is fairly popular (Campbell and Thompson, 2008; Fisher et al., 2015; Meese and Rogoff, 1983), mainly because forecasting errors are understated by in-sample errors and the best in-sample fit may not be able to accurately predict post-sample data (Bartolomei and Sweet, 1989; Pant and Starbuck, 1990; Tashman, 2000). Fildes and Makridakis (1995) were of the opinion that model performance on out-of-sample data was the benchmark for its utility in all applications.
A regression tree-based diagnostic approach is developed to evaluate factors affecting US wastewater treatment plant compliance with ammonia discharge permit limits using Discharge Monthly Report (DMR) data from a sample of 106 municipal treatment plants for the period of 2004–2008. Predictor variables used to fit the regression tree are selected using random forests, and consist of the previous month's effluent ammonia, influent flow rates and plant capacity utilization. The tree models are first used to evaluate compliance with existing ammonia discharge standards at each facility and then applied assuming more stringent discharge limits, under consideration in many states. The model predicts that the ability to meet both current and future limits depends primarily on the previous month's treatment performance. With more stringent discharge limits predicted ammonia concentration relative to the discharge limit, increases. In-sample validation shows that the regression trees can provide a median classification accuracy of > 70%. The regression tree model is validated using ammonia discharge data from an operating wastewater treatment plant and is able to accurately predict the observed ammonia discharge category approximately 80% of the time, indicating that the regression tree model can be applied to predict compliance for individual treatment plants providing practical guidance for utilities and regulators with an interest in controlling ammonia discharges. The proposed methodology is also used to demonstrate how to delineate reliable sources of demand and supply in a point source-to-point source nutrient credit trading scheme, as well as how planners and decision makers can set reasonable discharge limits in future.
Exponential smoothing: The state of the art-Part II
2006, International Journal of Forecasting
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A special case of EWQR was developed by Cipra (1992), who extended GES to the median by replacing the DLS criterion with discounted least absolute deviations. The only other GES research since 1985 is by Bartolomei and Sweet (1989), who compared GES to the A-A and A-M methods using 47 time series from the M1 competition (Makridakis et al., 1982). The authors found little difference in forecast accuracy, although they speculated that one of the damped-trend methods might have done better.
In Gardner [Gardner, E. S., Jr. (1985). Exponential smoothing: The state of the art. Journal of Forecasting 4, 1–28], I reviewed the research in exponential smoothing since the original work by Brown and Holt. This paper brings the state of the art up to date. The most important theoretical advance is the invention of a complete statistical rationale for exponential smoothing based on a new class of state-space models with a single source of error. The most important practical advance is the development of a robust method for smoothing damped multiplicative trends. We also have a new adaptive method for simple smoothing, the first such method to demonstrate credible improved forecast accuracy over fixed-parameter smoothing. Longstanding confusion in the literature about whether and how to renormalize seasonal indices in the Holt–Winters methods has finally been resolved. There has been significant work in forecasting for inventory control, including the development of new predictive distributions for total lead-time demand and several improved versions of Croston's method for forecasting intermittent time series. Regrettably, there has been little progress in the identification and selection of exponential smoothing methods. The research in this area is best described as inconclusive, and it is still difficult to beat the application of a damped trend to every time series.
Exponential smoothing model selection for forecasting
2006, International Journal of Forecasting
Applications of exponential smoothing to forecasting time series usually rely on three basic methods: simple exponential smoothing, trend corrected exponential smoothing and a seasonal variation thereof. A common approach to selecting the method appropriate to a particular time series is based on prediction validation on a withheld part of the sample using criteria such as the mean absolute percentage error. A second approach is to rely on the most appropriate general case of the three methods. For annual series this is trend corrected exponential smoothing: for sub-annual series it is the seasonal adaptation of trend corrected exponential smoothing. The rationale for this approach is that a general method automatically collapses to its nested counterparts when the pertinent conditions pertain in the data. A third approach may be based on an information criterion when maximum likelihood methods are used in conjunction with exponential smoothing to estimate the smoothing parameters. In this paper, such approaches for selecting the appropriate forecasting method are compared in a simulation study. They are also compared on real time series from the M3 forecasting competition. The results indicate that the information criterion approaches provide the best basis for automated method selection, the Akaike information criteria having a slight edge over its information criteria counterparts.
25 years of time series forecasting
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We review the past 25 years of research into time series forecasting. In this silver jubilee issue, we naturally highlight results published in journals managed by the International Institute of Forecasters (Journal of Forecasting 1982–1985 and International Journal of Forecasting 1985–2005). During this period, over one third of all papers published in these journals concerned time series forecasting. We also review highly influential works on time series forecasting that have been published elsewhere during this period. Enormous progress has been made in many areas, but we find that there are a large number of topics in need of further development. We conclude with comments on possible future research directions in this field.
Out-of-sample tests of forecasting accuracy: An analysis and review
2000, International Journal of Forecasting
Citation Excerpt :
The second aspect to the argument is that methods selected by best in-sample fit may not best predict post-sample data. Bartolomei and Sweet (1989) and Pant and Starbuck (1990) provide particularly convincing evidence on this point. One way to ascertain post-sample forecasting performance is to wait and see in real time.
In evaluations of forecasting accuracy, including forecasting competitions, researchers have paid attention to the selection of time series and to the appropriateness of forecast-error measures. However, they have not formally analyzed choices in the implementation of out-of-sample tests, making it difficult to replicate and compare forecasting accuracy studies. In this paper, I (1) explain the structure of out-of-sample tests, (2) provide guidelines for implementing these tests, and (3) evaluate the adequacy of out-of-sample tests in forecasting software. The issues examined include series-splitting rules, fixed versus rolling origins, updating versus recalibration of model coefficients, fixed versus rolling windows, single versus multiple test periods, diversification through multiple time series, and design characteristics of forecasting competitions. For individual time series, the efficiency and reliability of out-of-sample tests can be improved by employing rolling-origin evaluations, recalibrating coefficients, and using multiple test periods. The results of forecasting competitions would be more generalizable if based upon precisely described groups of time series, in which the series are homogeneous within group and heterogeneous between groups. Few forecasting software programs adequately implement out-of-sample evaluations, especially general statistical packages and spreadsheet add-ins.
Cross validation for uncertain autoregressive model
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^∗: Sonia M. BARTOLOMEI holds a B.S. in Industrial Engineering from the University of Puerto Rico (Mayagüez) and an M.S. in Industrial Engineering from Purdue University. She is currently as assistant professor in the Department of Industrial Engineering Technology at the Regional College of the University of Puerto Rico at Mayagüez.

^∗∗: Arnold L. SWEET has been Professor of Industrial Engineering at Purdue University since 1980. His interests are in the fields of stochastic processes, time series forecasting, statistical quality control, and applications of probability theory to problems of engineering interest. He is a member of IIE, ASQC, TIMS, and the International Institute of Forecasters.

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A note on a comparison of exponential smoothing methods for forecasting seasonal series

Abstract

A comparison of exponential smoothing methods for forecasting seasonal series

Computer tape containing the 1001 original time series

Exponential smoothing: the state of the art

Journal of Forecasting

Forecasting trends in time series

Management Science

The accuracy of extrapolation (time series) methods; results of a forecasting competition

Journal of Forecasting