Combination of Multi Level Forecasts
This paper provides a discussion of the effects of different multi-level learning approaches on the resulting out of sample forecast errors in the case of difficult real-world forecasting problems with large noise terms in the training data, frequently occurring structural breaks and quickly changing environments. In order to benefit from the advantages of learning on different aggregation levels and to reduce the risks of high noise terms on low level predictions and overgeneralization on higher levels, various approaches of using information at different levels are analysed in relation to their effects on the bias, variance and Bayes error components proposed by James and Hastie. We provide an extension of this decomposition for the multi-level case. An extensive analysis is also carried out answering the question of why the combination of predictions using information learned at different levels constitutes a significantly better approach in comparison to using only the predictions generated at one of the levels or other multi-level approaches. Additionally we argue why multi-level combinations should be used in addition to thick modelling and the use of different function spaces. Significant forecast improvements have been obtained when using the proposed multi-level combination approaches.
Keywordsmulti level forecasting forecast combination bias variance Bayes error decomposition revenue management
Unable to display preview. Download preview PDF.
- 2.G. James and T. Hastie, “Generalisations of the Bias/Variance Decomposition for Prediction Error”, technical report, http://www.stat.stanford.edu/~gareth/ftp/papers/bv.ps, 1996.
- 3.T. D. Russell and E. E. Adam, “An Empirical Evaluation of Alternative Forecast Combinations,” Eur. J. Oper. Res. Econ., vol. 33, 1987, pp. 1267–1276.Google Scholar
- 5.A. G. Timmermann, “Forecast Combinations”, Discussion paper no. 5361, http://www.cepr.org/pubs/dps/DP5361.asp, 2005.
- 6.S. Makridakis et al., “The m2 Competition: A Real-Time Judgementally Based Forecasting Study”, Int. J. Forecast., vol. 9, 1993, pp. 5–22.Google Scholar
- 10.J. V. Hansen, “Combining Predictors. Meta Machine Learning Methods and Bias/Variance and Ambiguity Decompositions,” Ph.D. dissertation, 2000.Google Scholar
- 12.R. G. Cross, “Revenue Management,” Broadway Books, 1997.Google Scholar
- 13.McGill and van Ryzin, “Revenue Management: Research Overview and Prospects,” Transp. Sci., vol. 33, no. 4, 1999.Google Scholar
- 16.S. Riedel and B. Gabrys, “Hierarchical Multilevel Approaches of Forecast Combination,” Proceedings of the OR 2004 conference, The Netherlands, 2004.Google Scholar
- 17.S. Riedel and B. Gabrys, “Evolving Multilevel Forecast Combination Models—An Experimental Study,” Proceedings of NiSIS 2005 Symposium, Albufeira, Portugal, 2005.Google Scholar
- 18.S. Riedel and B. Gabrys, “Adaptive Mechanisms in an Airline Ticket Demand Forecasting System,” Proceedings of the EUNITE 2003 conference, Oulu, Finland, 2003.Google Scholar