The combination of forecasts resulting from an ensemble of neural networks has been shown to outperform the use of a single "best" network model. This is supported by an extensive body of literature, which shows that combining generally leads to improvements in forecasting accuracy and robustness, and that using the mean operator often outperforms more complex methods of combining forecasts. This paper proposes a mode ensemble operator based on kernel density estimation, which unlike the mean operator is insensitive to outliers and deviations from normality, and unlike the median operator does not require symmetric distributions. The three operators are compared empirically and the proposed mode ensemble operator is found to produce the most accurate forecasts, followed by the median, while the mean has relatively poor performance. The findings suggest that the mode operator should be considered as an alternative to the mean and median operators in forecasting applications. Experiments indicate that mode ensembles are useful in automating neural network models across a large number of time series, overcoming issues of uncertainty associated with data sampling, the stochasticity of neural network training and the distribution of the forecasts.

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Modelling artificial neural networks (NN) for accurate time series prediction poses multiple challenges, in particular specifying the network architecture in accordance with the underlying structure of the time series. The data generating processes may exhibit a variety of stochastic or deterministic time series patterns of single or multiple seasonality, trends and cycles, overlaid with pulses, level shifts and structural breaks, all depending on the discrete time frequency in which it is observed. For heterogeneous datasets of time series, such as the 2008 ESTSP competition, a universal methodology is required for automatic network specification across varying data patterns and time frequencies. We propose a fully data driven forecasting methodology that combines filter and wrapper approaches for feature evaluation, construction and transformation. The methodology identifies time series patterns, creates and transforms explanatory variables and specifies multilayer perceptrons for heterogeneous sets of time series without expert intervention. Examples of the valid and reliable performance in comparison to established benchmark methods are shown for a set of synthetic time series and for the ESTSP"08 competition dataset, where the proposed methodology obtained second place.

From its foundation, operational research (OR) has made many substantial contributions to practical forecasting in organizations. Equally, researchers in other disciplines have influenced forecasting practice. Since the last survey articles in JORS, forecasting has developed as a discipline with its own journals. While the effect of this increased specialization has been a narrowing of the scope of OR's interest in forecasting, research from an OR perspective remains vigorous. OR has been more receptive than other disciplines to the specialist research published in the forecasting journals, capitalizing on some of their key findings. In this paper, we identify the particular topics of OR interest over the past 25 years. After a brief summary of the current research in forecasting methods, we examine those topic areas that have grabbed the attention of OR researchers: computationally intensive methods and applications in operations and marketing. Applications in operations have proved particularly important, including the management of inventories and the effects of sharing forecast information across the supply chain. The second area of application is marketing, including customer relationship management using data mining and computer-intensive methods. The paper concludes by arguing that the unique contribution that OR can continue to make to forecasting is through developing models that link the effectiveness of new forecasting methods to the organizational context in which the models will be applied. The benefits of examining the system rather than its separate components are likely to be substantial.