International Journal of Forecasting 27 (2011) 238–251 www.elsevier.com/locate/ijforecast Combining exponential smoothing forecasts using Akaike weights Stephan Kolassa SAF AG, High-Tech-Center 2, Bahnstrasse 1, 8274 T¨ agerwilen, Switzerland Abstract Simple forecast combinations such as medians and trimmed or winsorized means are known to improve the accuracy of point forecasts, and Akaike’s Information Criterion (AIC) has given rise to so-called Akaike weights, which have been used successfully to combine statistical models for inference and prediction in specialist fields, e.g., ecology and medicine. We examine combining exponential smoothing point and interval forecasts using weights derived from AIC, small-sample-corrected AIC and BIC on the M1 and M3 Competition datasets. Weighted forecast combinations perform better than forecasts selected using information criteria, in terms of both point forecast accuracy and prediction interval coverage. Simple combinations and weighted combinations do not consistently outperform one another, while simple combinations sometimes perform worse than single forecasts selected by information criteria. We find a tendency for a longer history to be associated with a better prediction interval coverage. c ⃝ 2010 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved. Keywords: AIC; BIC; Combining forecasts; Information criteria; Model selection 1. Introduction Exponential smoothing and state space models (Hyndman, Koehler, Ord, & Snyder, 2008; Hynd- man, Koehler, Snyder, & Grose, 2002) have been the workhorses of forecasters for a long time. Smoothing methods are classified depending on whether an addi- tive or multiplicative trend is used, whether the trend is damped or not and whether additive or multiplica- tive seasonality is used (Gardner, 2006). These meth- ods have a solid statistical foundation (Hyndman et al., 2008), are quite simple in their application and have performed very well in various forecasting competi- E-mail address: Stephan.Kolassa@saf-ag.com. tions (Makridakis et al., 1982; Makridakis & Hibon, 2000). Given these advantages of exponential smoothing methods and the large number of possible models available to choose from, attention has naturally fo- cused on the best way of identifying the model with the optimal predictive performance for a given time series. Akaike’s Information Criterion (AIC; Akaike, 1973, 1974; Parzen, Tanabe, & Kitagawa, 1998) is de- fined as AIC =−2 log L + 2 p for a model with likelihood L and p parameters. Akaike (1974, see also Konishi & Kitagawa, 2008, 0169-2070/$ - see front matter c ⃝ 2010 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.ijforecast.2010.04.006