Dynamic Pooling for the Combination of Forecasts Generated Using Multi Level Learning

In this paper we provide experimental results and extensions to our previous theoretical findings concerning the combination of forecasts that have been diversified by three different methods: with parameters learned at different data aggregation levels, by thick modeling and by the use of different forecasting methods. An approach of error variance based pooling as proposed by Aiolfi and Timmermann has been compared with flat combinations as well as an alternative pooling approach in which we consider information about the used diversification. An 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 corresponding to the different types of diversification. We describe different evolutionary approaches in order to evolve the order of pooling of the diversification dimensions. Extensions of such evolutions allow the generation of more flexible multi level multi step combination structures containing better adaptive capabilities. We could prove a significant error reduction comparing results of our generated combination structures with results generated with the algorithm of Aiolfi and Timmermann as well as with flat combination for the application of Revenue Management seasonal forecasting

Forecast combination in revenue management demand forecasting.

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

Performance of Deterministic and Probabilistic Hydrological Forecasts for the Short-Term Optimization of a Tropical Hydropower Reservoir

Hydropower is the most important source of electricity in Brazil. It is subject to the natural variability of water yield. One building block of the proper management of hydropower assets is the short-term forecast of reservoir inflows as input for an online, event-based optimization of its release strategy. While deterministic forecasts and optimization schemes are the established techniques for short-term reservoir management, the use of probabilistic ensemble forecasts and multi-stage stochastic optimization techniques is receiving growing attention. The present work introduces a novel, mass conservative scenario tree reduction in combination with a detailed hindcasting and closed-loop control experiments for a multi-purpose hydropower reservoir in a tropical region in Brazil. The case study is the hydropower project Três Marias, which is operated with two main objectives: (i) hydroelectricity generation and (ii) flood control downstream. In the experiments, precipitation forecasts based on observed data, deterministic and probabilistic forecasts are used to generate streamflow forecasts in a hydrological model over a period of 2 years. Results for a perfect forecast show the potential benefit of the online optimization and indicate a desired forecast lead time of 30 days. In comparison, the use of actual forecasts of up to 15 days shows the practical benefit of operational forecasts, where stochastic optimization (15 days lead time) outperforms the deterministic version (10 days lead time) significantly. The range of the energy production rate between the different approaches is relatively small, between 78% and 80%, suggesting that the use of stochastic optimization combined with ensemble forecasts leads to a significantly higher level of flood protection without compromising the energy production

Combining forecasts based on multiple encompassing tests in a macroeconomic core system

Copyright © 2010 John Wiley & Sons, Ltd. This is the accepted version of the following article: Costantini, M. and Kunst, R. M. (2011), Combining forecasts based on multiple encompassing tests in a macroeconomic core system. J. Forecast., 30: 579–596, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/for.1190/abstract.This paper investigates whether and to what extent multiple encompassing tests may help determine weights for forecast averaging in a standard vector autoregressive setting. To this end we consider a new test-based procedure, which assigns non-zero weights to candidate models that add information not covered by other models. The potential benefits of this procedure are explored in extensive Monte Carlo simulations using realistic designs that are adapted to UK and to French macroeconomic data, to which trivariate vector autoregressions (VAR) are fitted. Thus simulations rely on potential data-generating mechanisms for macroeconomic data rather than on simple but artificial designs. We run two types of forecast ‘competitions’. In the first one, one of the model classes is the trivariate VAR, such that it contains the generating mechanism. In the second specification, none of the competing models contains the true structure. The simulation results show that the performance of test-based averaging is comparable to uniform weighting of individual models. In one of our role model economies, test-based averaging achieves advantages in small samples. In larger samples, pure prediction models outperform forecast averages

Forecasting GDP at the regional level with many predictors

In this paper, we assess the accuracy of macroeconomic forecasts at the regional level using a large data set at quarterly frequency. We forecast gross domestic product (GDP) for two German states (Free State of Saxony and Baden- Württemberg) and Eastern Germany. We overcome the problem of a ’data-poor environment’ at the sub-national level by complementing various regional indicators with more than 200 national and international indicators. We calculate single– indicator, multi–indicator, pooled and factor forecasts in a pseudo real–time setting. Our results show that we can significantly increase forecast accuracy compared to an autoregressive benchmark model, both for short and long term predictions. Furthermore, regional indicators play a crucial role for forecasting regional GDP

Do We Need Experts for Time Series Forecasting?

This study examines a selection of off-the-shelf forecastingand forecast combination algorithms with a focus on assessing their practical relevance by drawing conclusions for non-expert users. Some of the methods have only recently been introduced and have not been part in comparative empirical evaluations before. Considering the advances of forecasting techniques, this analysis addresses the question whether we need human expertise for forecasting or whether the investigated methods provide comparable performance

Forecasting and Forecast Combination in Airline Revenue Management Applications

Predicting a variable for a future point in time helps planning for unknown future situations and is common practice in many areas such as economics, finance, manufacturing, weather and natural sciences. This paper investigates and compares approaches to forecasting and forecast combination that can be applied to service industry in general and to airline industry in particular. Furthermore, possibilities to include additionally available data like passenger-based information are discussed

Measuring output gap uncertainty

We propose a methodology for producing density forecasts for the output gap in real time using a large number of vector autoregessions in inflation and output gap measures. Density combination utilizes a linear mixture of experts framework to produce potentially non-Gaussian ensemble densities for the unobserved output gap. In our application, we show that data revisions alter substantially our probabilistic assessments of the output gap using a variety of output gap measures derived from univariate detrending filters. The resulting ensemble produces well-calibrated forecast densities for US inflation in real time, in contrast to those from simple univariate autoregressions which ignore the contribution of the output gap. Combining evidence from both linear trends and more flexible univariate detrending filters induces strong multi-modality in the predictive densities for the unobserved output gap. The peaks associated with these two detrending methodologies indicate output gaps of opposite sign for some observations, reflecting the pervasive nature of model uncertainty in our US data