Guaranteed Stability of Autoregressive Models with Granger Causality Learned from Wald Tests
This paper aims to explain relationships between time series by using the Granger causality (GC) concept through autoregressive (AR) models and to assure the model stability. Examining such GC relationship is performed on the model parameters using the Wald test and the model stability is guaranteed by the infinity-norm constraint on the dynamic matrix of the AR process. The proposed formulation is a least-squares estimation with Granger causality and stability constraints which is a convex program with a quadratic objective subject to linear equality and inequality norm constraints. We show by simulations that various typical factors could lead to unstable estimated models when using an unconstrained method. Estimated models from our approach are guaranteed to be stable but the model fitting error could be conservatively increased due to the selected stability condition.
Authors who publish with Engineering Journal agree to transfer all copyright rights in and to the above work to the Engineering Journal (EJ)'s Editorial Board so that EJ's Editorial Board shall have the right to publish the work for nonprofit use in any media or form. In return, authors retain: (1) all proprietary rights other than copyright; (2) re-use of all or part of the above paper in their other work; (3) right to reproduce or authorize others to reproduce the above paper for authors' personal use or for company use if the source and EJ's copyright notice is indicated, and if the reproduction is not made for the purpose of sale.