Bootstrapping stationary invertible VARMA models in echelon form: A simulation evidence1

In this paper we propose bootstrapping Hannan and Rissanen (1982) estimators in stationary invertible VARMA models, with known order (p, q). Although we consider bootstrapping such models under the echelon form parameterization, the results we derive herein remain valid to other alternative identification issues. In particular, we shall exploit the theoretical developments stated in Dufour and Jouini (2005) and Dufour and Jouini (2008) to establish the asymptotic validity of bootstrapping such models for parametric and nonparametric bootstrap methods to approximating the joint distribution of the echelon form VARMA parameter estimates. The finite sample accuracy of our proposed method is evaluated through a Monte Carlo (MC) simulation, specifically, by further studying the echelon form VARMA parameter confidence interval empirical coverage rates.