Forecast combination in revenue management demand forecasting.

Abstract

The domain of multi level forecast combination is a challenging new domain containing a large potential for forecast improvements. This thesis presents a theoretical and experimental analysis of different types of forecast diversification on forecast error covariances and resulting combined forecast quality. Three types of diversification are used: (a) diversification concerning the level of learning (b) diversification of predefined parameter values and (c) the use of different forecast models. The diversification is carried out on forecasts of seasonal factor predictions in Revenue Management for Airlines. After decomposing the data and generating diversified forecasts a (multi step) combination procedure is applied. We provide theoretical evidence of why and under which conditions multi step multi level forecast combination can be a powerful approach in order to build a high quality and adaptive forecast system. We theoretically and experimentally compare models differing with respect to the used decomposition, diversification as well as the applied combination models and structures. After an introduction into the application of forecasting seasonal behaviour in Revenue Management, a literature review of the theory of forecast combination is provided. In order to get a clearer idea of under which condition combination works, we then investigate aspects of forecast diversity and forecast diversification. The diversity of forecast errors in terms of error covariances can be expressed in a decomposed manner in relation to different independent error components. This type of decomposed analysis has the advantage that it allows conclusions concerning the potential of the diversified forecasts for future combination. We carry out such an analysis of effects of different types of diversification on error components corresponding to the bias-variance-Bayes decomposition proposed by James and Hastie. Different approaches of how to include information from different levels into forecasting are also discussed in the thesis. The improvements achieved with multi level forecast combination prove that theoretical analysis is extremely important in this relatively new field. The bias-variance-Bayes decomposition is extended to the multi level case. An analysis of the effects of including forecasts with parameters learned at different levels on the bias and variance error components show that forecast combination is the best choice in comparison to some other discussed alternatives. The proposed approach represents a completely automatic procedure. It realises changes in the error components which are not only advantageous at the low level, but have also a stabilising effect on aggregates of low level forecasts to the higher level. We also identify cases in which multi level forecast combination should ideally be connected with the use of different function spaces and/or thick modelling related to certain parameter values or preprocessing procedures. In order to avoid problems occurring for large sets of highly correlated forecasts when considering covariance information, we investigated the potential of pooling and trimming for our case. We estimate the expected behaviour of our diversified forecasts in purely error variance based pooling represented by a common approach of Aiolfi and Timmermann and analyse effects of different kinds of covariances on the accuracy of the combined forecast. We show that a significant loss in the expected forecast accuracy may ensue because of typical inhomogeneities in the covariance matrix for the analysed case. If covariance information is available in a sufficiently high quality, it is possible to run a clustering directly based on covariance information. We discuss how to carry out a clustering in that case. We also consider a case (quite common in our application) when covariance information may not be available and propose a novel simplified representation of the covariance matrix which represents the distance in the forecast generation space and is only based on knowledge about the forecast generation process. A new pooling approach is proposed that avoids inhomogeneities in the covariance matrix by considering the information contained in the simplified covariance representation. One of the main advantages of the proposed approach is that the covariance matrix does not have to be calculated. We compared the results of our approach with the approach of Aiolfi and Timmermann and explained the reasons for significant improvement. Another advantage of our approach is that it leads to the generation of novel multi step, multi level forecast generation structures that carry out the combination in different steps of pooling. Finally, we describe different evolutionary approaches in order to generate combination structures automatically. We investigate very flexible approaches as well as approaches that avoid the expected inhomogeneities in the error covariance matrix based on our theoretical findings. The theoretical analysis is supported by experimental results. We could achieve an improvement of forecast quality up to 11 percent for the practical application of demand forecasting in Revenue Management compared to the current optimised forecasting system.