Collections of time series often exhibit hierarchical structures, which are linear constraints that allow higher levels of series to be disaggregated to lower levels. The property that the forecasts also add up corresponding to the aggregation structure is referred to as coherency.
Traditional approaches achieve coherency by forecasting a single level of time series and rearranging it to obtain forecasts of all levels based on the structure. In contrast to traditional approaches, forecasting reconciliation combines forecasts for all levels of time series in the collection. It makes use of correlations across levels of the hierarchy that the traditional methods overlook to improve the accuracy of the forecasts.
In this paper, we expand the reconciliation technique to also include the forecasts of general linear combinations of series, known as components. A set of components that makes use of the underlying interaction between series and aims at increasing forecast accuracy can improve the performance of reconciliation.
We explore two sets of components. The first one is from the well known principal component analysis because of its well-studied properties and relatively efficient computation. The second one is from forecastable component analysis (ForeCA), which aims to maximise a measure of forecastability calculated from the Shannon entropy of the spectral density. We introduce an efficient computing method of using ForeCA in forecast reconciliation. Performance of the proposed method is evaluated using simulation data and Australian tourism data.