Combining time series models for forecasting

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142 Scopus citations


Statistical models (e.g., ARIMA models) have commonly been used in time series data analysis and forecasting. Typically, one model is selected based on a selection criterion (e.g., AIC), hypothesis testing, and/or graphical inspection. The selected model is then used to forecast future values. However, model selection is often unstable and may cause an unnecessarily high variability in the final estimation/prediction. In this work, we propose the use of an algorithm, AFTER, to convexly combine the models for a better performance of prediction. The weights are sequentially updated after each additional observation. Simulations and real data examples are used to compare the performance of our approach with model selection methods. The results show an advantage of combining by AFTER over selection in terms of forecasting accuracy at several settings.

Original languageEnglish (US)
Pages (from-to)69-84
Number of pages16
JournalInternational Journal of Forecasting
Issue number1
StatePublished - Jan 2004

Bibliographical note

Funding Information:
The authors thank the reviewers for very helpful comments and suggestions, which led to a significant improvement of the paper. This research was supported by the United States National Science Foundation CAREER Award Grant DMS0094323.


  • Combining forecasts
  • Forecast instability
  • Model selection
  • Modeling


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