In many applications, there are multiple time series that are hierarchically organized and can be aggregated at several different levels in groups based on products, geography or some other features. We call these "hierarchical time series". They are commonly forecast using either a "bottom-up" or a "top-down" method. In this paper we propose a new approach to hierarchical forecasting which provides optimal forecasts that are better than forecasts produced by either a top-down or a bottom-up approach. Our method is based on independently forecasting all series at all levels of the hierarchy and then using a regression model to optimally combine and reconcile these forecasts. The resulting revised forecasts add up appropriately across the hierarchy, are unbiased and have minimum variance amongst all combination forecasts under some simple assumptions. We show in a simulation study that our method performs well compared to the top-down approach and the bottom-up method. We demonstrate method by forecasting Australian tourism demand where the data are disaggregated by purpose of visit and geographical region.

In this paper we explore the hierarchical nature of tourism demand time series and produce short-term forecasts for Australian domestic tourism. The data and forecasts are organized in a hierarchy based on disaggregating the data for different geographical regions and for different purposes of travel. We consider five approaches to hierarchical forecasting: two variations of the top-down approach, the bottom-up method, a newly proposed top-down approach where top-level forecasts are disaggregated according to forecasted proportions of lower level series, and a recently proposed optimal combination approach. Our forecast performance evaluation shows that the top-down approach based on forecast proportions and the optimal combination method perform best for the tourism hierarchies we consider. By applying these methods, we produce detailed forecasts for the Australian domestic tourism market.

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Disease risk prediction tools are used for population screening and to guide clinical care. They identify which individuals have particularly elevated risk of disease. The development of a new risk prediction tool involves several methodological components including: selection of a general modelling framework and specific functional form for the new tool, making decisions about the inclusion of risk factors, dealing with missing data in those risk factors, and performing validation checks of a new tool's performance. There have been many methodological developments of relevance to these issues in recent years. Developments of importance for disease detection in humans were reviewed and their uptake in risk prediction tool development illustrated. This review leads to guidance on appropriate methodology for future risk prediction development activities.