Fotios Petropoulos

Fotios Petropoulos, Daniele Apiletti, Vassilios Assimakopoulos et al.

Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number of forecasting applications calls for a diverse set of forecasting methods to tackle real-life challenges. This article provides a non-systematic review of the theory and the practice of forecasting. We provide an overview of a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts. We do not claim that this review is an exhaustive list of methods and applications. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of forecasting theory and practice. Given its encyclopedic nature, the intended mode of reading is non-linear. We offer cross-references to allow the readers to navigate through the various topics. We complement the theoretical concepts and applications covered by large lists of free or open-source software implementations and publicly-available databases.

Yanfei Kang, Wei Cao, Fotios Petropoulos et al.

Forecast combinations have been widely applied in the last few decades to improve forecasting. Estimating optimal weights that can outperform simple averages is not always an easy task. In recent years, the idea of using time series features for forecast combination has flourished. Although this idea has been proved to be beneficial in several forecasting competitions, it may not be practical in many situations. For example, the task of selecting appropriate features to build forecasting models is often challenging. Even if there was an acceptable way to define the features, existing features are estimated based on the historical patterns, which are likely to change in the future. Other times, the estimation of the features is infeasible due to limited historical data. In this work, we suggest a change of focus from the historical data to the produced forecasts to extract features. We use out-of-sample forecasts to obtain weights for forecast combinations by amplifying the diversity of the pool of methods being combined. A rich set of time series is used to evaluate the performance of the proposed method. Experimental results show that our diversity-based forecast combination framework not only simplifies the modelling process but also achieves superior forecasting performance in terms of both point forecasts and prediction intervals. The value of our proposition lies on its simplicity, transparency, and computational efficiency, elements that are important from both an optimisation and a decision analysis perspective.

Evangelos Spiliotis, Mahdi Abolghasemi, Rob J Hyndman et al.

Hierarchical forecasting methods have been widely used to support aligned decision-making by providing coherent forecasts at different aggregation levels. Traditional hierarchical forecasting approaches, such as the bottom-up and top-down methods, focus on a particular aggregation level to anchor the forecasts. During the past decades, these have been replaced by a variety of linear combination approaches that exploit information from the complete hierarchy to produce more accurate forecasts. However, the performance of these combination methods depends on the particularities of the examined series and their relationships. This paper proposes a novel hierarchical forecasting approach based on machine learning that deals with these limitations in three important ways. First, the proposed method allows for a non-linear combination of the base forecasts, thus being more general than the linear approaches. Second, it structurally combines the objectives of improved post-sample empirical forecasting accuracy and coherence. Finally, due to its non-linear nature, our approach selectively combines the base forecasts in a direct and automated way without requiring that the complete information must be used for producing reconciled forecasts for each series and level. The proposed method is evaluated both in terms of accuracy and bias using two different data sets coming from the tourism and retail industries. Our results suggest that the proposed method gives superior point forecasts than existing approaches, especially when the series comprising the hierarchy are not characterized by the same patterns.