Identification of Vector Autoregressive Models with Granger and Stability Constraints

In this work, we introduce an iterative method for the estimation of vector autoregressive (VAR) models with Granger and stability constraints. When the order of the model $(p)$ and the Granger sparsity pattern (GSP) are not known, the newly proposed method is integrated in a two-stage approach. An information theoretic (IT) criterion is used in the first stage for selecting the value of p. In the second stage, a set of possible candidates for GSP are produced by applying the Wald test, and the best one is chosen with an IT criterion. In experiments with synthetic data, we demonstrate that our method yields more accurate forecasts than the state-of-art algorithm that is based on convex optimization and fits models which are guaranteed to be stable.