Joint Bottom-Up Method for Hierarchical Time-Series: Application to Australian Tourism

Abstract

Many applications involve a hierarchy of time-series, where values at the bottom level aggregate to values at higher levels. Forecasts of such hierarchical data need to be accurate, probabilistic, and coherent in the sense of respecting hierarchical aggregation. While recent developments have explicitly modeled every time-series in the hierarchy, we show, under general conditions, that hierarchical data can be modeled jointly by considering only its bottom-level series and their contemporaneous covariance. Inspired by this result, we devise a Bayesian method that models bottom-level 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 reveals the hidden spatio-temporal dynamics of different types 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