Joint Bottom-Up Method for Forecasting Grouped Time Series: Application to Australian Domestic Tourism

Abstract

Many applications involve grouped time series, where values of some series sum to the values of other series based on geography, product category, or other features. Forecasts of such data need to be accurate, probabilistic, and coherent in the sense of respecting the aggregation constraints. While recent developments have explicitly modeled every time series, we show that under general conditions it is sufficient to consider the most disaggregated series and their contemporaneous covariance. Inspired by this result, we devise a Bayesian method that models the most disaggregated series jointly, takes into account their contemporaneous covariance, and performs automatic selection of lag terms, both within and across series. The model copes with high-dimensional data, and outputs both point and probabilistic forecasts. Additionally, it returns posterior distributions of all parameters, which can be used for inference. As a case study, we apply our method to make recommendations on planning and promotion of domestic tourism in Australia. Our model outperforms common state-of-the-art techniques in terms of prediction accuracy, reveals the hidden spatio-temporal dynamics of domestic tourism in Australia, and allows us to explore how promotional investments could be localized to develop tourism in accordance with the declared desiderata of the Australian government.

Keywords: Bayesian statistics, Dimensionality reduction, Multivariate autoregressive models, Probabilistic forecasting, Spike-and-slab