A sparsity-controlled vector autoregressive model

Abstract

Vector autoregressive (VAR) models constitute a powerful and well studied tool to analyze multivariate time series. Since sparseness, crucial to identify and visualize joint dependencies and relevant causalities, is not expected to happen in the standard VAR model, several sparse variants have been introduced in the literature. However, in some cases it might be of interest to control some dimensions of the sparsity, as e.g. the number of causal features allowed in the prediction. To authors extent none of the existent methods endows the user with full control over the different aspects of the sparsity of the solution. In this paper we propose a sparsity-controlled VAR model which allows to control different dimensions of the sparsity, enabling a proper visualization of potential causalities and dependencies. The model coefficients are found as the solution to a mathematical optimization problem, solvable by standard numerical optimization routines. The tests performed on both simulated and real-life multivariate time series show that our approach may outperform both the standard and Group Lasso in terms of prediction errors specially when highly sparse graphs are sought, while avoiding the VAR’s overfitting for more dense graphs. Causality; Mixed Integer Non Linear Programming; multivariate time series; sparse models; Vector autoregressive process.