Abstract
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 our proposed method by forecasting Australian tourism demand where the data are disaggregated by purpose of travel and geographical region.
Highlights
In business and economics, there are often applications requiring forecasts of many related time series organized in a hierarchical structure based on dimensions, such as product and geography
We propose a new statistical method for forecasting hierarchical time series which (1) provides point forecasts that are reconciled across the levels of the hierarchy; (2) allows for the correlations and interaction between the series at each level of the hierarchy; (3) provides estimates of forecast uncertainty which are reconciled across the levels of hierarchy; and (4) is sufficiently flexible that ad hoc adjustments can be incorporated, information about individual series can be allowed for, and important covariates can be included
We have proposed a new statistical method for forecasting hierarchical time series, which allows optimal point forecasts to be produced that are reconciled across the levels of a hierarchy
Summary
There are often applications requiring forecasts of many related time series organized in a hierarchical structure based on dimensions, such as product and geography. Many businesses combine these methods (giving what is sometimes called the “middle-out” method) where forecasts are obtained for each series at an intermediate level of the hierarchy, and aggregation is used to obtain forecasts at higher levels and disaggregation is used to obtain forecasts at lower levels. Optimal combination forecasts for hierarchical time series argued that information loss is substantial in aggregation and the bottom-up method gives more accurate forecasts. Kahn (1998) suggested that it is time to combine the existing methodologies so that we can enjoy the good features of both methods, but no specific ideas were provided in that discussion Another very good discussion paper is Fliedner (2001), who summarizes the uses and application guidelines for hierarchical forecasting.
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