Sparse estimation of multi-class vector autoregressive models

Vector AutoRegressive (VAR) models form a special case of multivariate regression models in that the response variables are observed over time and modeled as a function of their own past values. Assume we have $K$ VAR models for $K$ distinct but related classes. We jointly estimate these $K$ VAR models to borrow strength across classes and to estimate multiple models that share certain characteristics. Our methodology encourages corresponding effects to be estimated similar across classes, while still allowing for small differences between them. Moreover, we focus on multi-class estimation of high-dimensional VAR models, i.e. models with a large number of time series relative to the time series length. Therefore, our estimate is sparse: unimportant effects are estimated as exactly zero, which facilitates the interpretation of the results. We consider a marketing application of the proposed methodology.status: publishe