A Top-Down Approach to Hierarchically Coherent Probabilistic Forecasting
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Hierarchical forecasting is a key problem in many practical multivariate forecasting applications - the goal is to obtain coherent predictions for a large number of correlated time series that are arranged in a pre-specified tree hierarchy. In this paper, we present a probabilistic top-down approach to hierarchical forecasting that uses a novel attention-based RNN model to learn the distribution of the proportions according to which each parent prediction is split among its children nodes at any point in time. These probabilistic proportions are then coupled with an independent univariate probabilistic forecasting model (such as Prophet or STS) for the root time series. The resulting forecasts are computed in a top-down fashion and are naturally coherent, and also support probabilistic predictions over all time series in the hierarchy. We provide theoretical justification for the superiority of our top-down approach compared to traditional bottom-up hierarchical modeling. Finally, we experiment on three public datasets and demonstrate significantly improved probabilistic forecasts, compared to state-of-the-art probabilistic hierarchical models.
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