This is joint work with Rickard Sandberg and looks at the implicit connections enforced by hierarchical time series forecasting, between the nodes of the hierarchy, contrasting them to VAR models that captures connections explicitly.
The four major Scandinavian economies (Denmark, Finland, Sweden and Norway) have high workforce mobility and depending on market dynamics the unemployment in one country can be influenced by conditions in the neighbouring ones. We provide evidence that Vector Autoregressive modelling of unemployment between the four countries produces more accurate predictions than constructing independent forecasting models. However, given the dimensionality of the VAR model its specification and estimation can become challenging, particularly when modelling unemployment across multiple factors. To overcome this we consider the hierarchical structure of unemployment in Scandinavia, looking at three dimensions: age, country and gender. This allows us to construct multiple complimentary hierarchies, aggregating across each dimension. The resulting grouped hierarchy enforces a well-defined structure to the forecasting problem. By producing forecasts across the hierarchy, under the restriction that they are reconciled across the hierarchical structure, we provide an alternative way to establish connections between the time series that describe the four countries. We demonstrate that this approach is not only competitive with VAR modelling, but as each series is modelled independently, we can easily employ advanced forecasting models, in which case independent and VAR forecasts are substantially outperformed. Our results illustrate that there are three useful alternatives to model connections between series, directly through multivariate vector models, through the covariance of the prediction errors across a hierarchy of series, and through the implicit restrictions enforced by the hierarchical structure. We provide evidence of the performance of each, as well as their combination.