Pooling information across levels in hierarchical time series forecasting via Kernel methods

In this paper, we present a novel method that extends the kernel-based support vector regression to hierarchical time series analysis. This predictive task consists of taking advantage of the hierarchical structure of a set of related time series. This is a common challenge in retail, for example, in which product sales are grouped according to categories with multiple levels. The proposed strategy constructs several predictors in a single optimization problem, pooling information across the different levels. In addition to the traditional two objectives included in support vector machines, model fit and Tikhonov regularization, data pooling is performed by including a third objective in the formulation. Originally presented as a linear method, a kernel machine is derived using duality theory. Experiments on benchmark datasets for hierarchical time series forecasting demonstrate the virtues of our all-together strategy over the well-known strategies for handling this task, namely, the bottom-up and top-down approaches.