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

Review of Nature-Inspired Forecast Combination Techniques

Effective and efficient planning in various areas can be significantly supported by forecasting a variable like an economy growth rate or product demand numbers for a future point in time. More than one forecast for the same variable is often available, leading to the question whether one should choose one of the single models or combine several of them to obtain a forecast with improved accuracy. In the almost 40 years of research in the area of forecast combination, an impressive amount of work has been done. This paper reviews forecast combination techniques that are nonlinear and have in some way been inspired by nature

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

Combinations of time series forecasts: when and why are they beneficial?.

Time series forecasting has a long track record in many application areas. In forecasting research, it has been illustrated that finding an individual algorithm that works best for all possible scenarios is hopeless. Therefore, instead of striving to design a single superior algorithm, current research efforts have shifted towards gaining a deeper understanding of the reasons a forecasting method may perform well in some conditions whilst it may fail in others. This thesis provides a number of contributions to this matter. Traditional empirical evaluations are discussed from a novel point of view, questioning the benefit of using sophisticated forecasting methods without domain knowledge. An own empirical study focusing on relevant off-the shelf forecasting and forecast combination methods underlines the competitiveness of relatively simple methods in practical applications. Furthermore, meta-features of time series are extracted to automatically find and exploit a link between application specific data characteristics and forecasting performance using meta-learning. Finally, the approach of extending the set of input forecasts by diversifying functional approaches, parameter sets and data aggregation level used for learning is discussed, relating characteristics of the resulting forecasts to different error decompositions for both individual methods and combinations. Advanced combination structures are investigated in order to take advantage of the knowledge on the forecast generation processes. Forecasting is a crucial factor in airline revenue management; forecasting of the anticipated booking, cancellation and no-show numbers has a direct impact on general planning of routes and schedules, capacity control for fareclasses and overbooking limits. In a collaboration with Lufthansa Systems in Berlin, experiments in the thesis are conducted on an airline data set with the objective of improving the current net booking forecast by modifying one of its components, the cancellation forecast. To also compare results achieved of the methods investigated here with the current state-of-the-art in forecasting research, some experiments also use data sets of two recent forecasting competitions, thus being able to provide a link between academic research and industrial practice

Graph-based Time Series Clustering for End-to-End Hierarchical Forecasting

Existing relationships among time series can be exploited as inductive biases in learning effective forecasting models. In hierarchical time series, relationships among subsets of sequences induce hard constraints (hierarchical inductive biases) on the predicted values. In this paper, we propose a graph-based methodology to unify relational and hierarchical inductive biases in the context of deep learning for time series forecasting. In particular, we model both types of relationships as dependencies in a pyramidal graph structure, with each pyramidal layer corresponding to a level of the hierarchy. By exploiting modern - trainable - graph pooling operators we show that the hierarchical structure, if not available as a prior, can be learned directly from data, thus obtaining cluster assignments aligned with the forecasting objective. A differentiable reconciliation stage is incorporated into the processing architecture, allowing hierarchical constraints to act both as an architectural bias as well as a regularization element for predictions. Simulation results on representative datasets show that the proposed method compares favorably against the state of the art

A loss discounting framework for model averaging and selection in time series models

We introduce a Loss Discounting Framework for model and forecast combination which generalises and combines Bayesian model synthesis and generalized Bayes methodologies. We use a loss function to score the performance of different models and introduce a multilevel discounting scheme which allows a flexible specification of the dynamics of the model weights. This novel and simple model combination approach can be easily applied to large scale model averaging/selection, can handle unusual features such as sudden regime changes, and can be tailored to different forecasting problems. We compare our method to both established methodologies and state of the art methods for a number of macroeconomic forecasting examples. We find that the proposed method offers an attractive, computationally efficient alternative to the benchmark methodologies and often outperforms more complex techniques

On Model-Selection and Applications of Multilevel Models in Survey and Causal Inference

This thesis includes three parts. The overarching theme is how to analyze multilevel structured datasets, particularly in the areas of survey and causal inference. The first part discusses model selection of hierarchical models, in the context of a national political survey. I found that the commonly used model selection criteria based on predictive accuracy, such as cross validation, don't perform very well in the case of political survey and explore the possible causes. The second part centers around a unique data set on the presidential election collected through an online platform. I show that with adequate modeling, meaningful and highly accurate information could be extracted from this highly-biased data set. The third part builds on a formal causal inference framework for group-structured data, such as meta-analysis and multi-site trials. In particular, I develop a Gaussian Process model under this framework and demonstrate additional insights that can be gained compared with traditional parametric models