Linear Estimation of Weak VARMA Models with a Macroeconomic Application

• Activity Number: 310
• Type: Contributed
• Date/Time: Wednesday, August 14, 2002 : 10:30 AM to 12:20 PM
• Sponsor: Business & Economics Statistics Section*
• Author(s): Denis Pelletier*+ and Jean-Marie Dufour
• Affiliation(s): Université de Montréal and Université de Montréal
• Keywords: linear regression ; VARMA ; final equation form ; information criterion ; strong mixing condition ; impulse response functions

Abstract

In this paper, we propose a linear estimation method in three steps for weak VARMA models. This paper is a generalization of the work of Hannan and Rissanen (1982), where the authors proposed a regression-based estimation method for univariate ARMA. We only assume that the innovations are uncorrelated and obey a strong mixing condition, instead of being independent or a martingale difference sequence. This allows us to broaden the class of models to which our method can be applied--e.g,. time-aggregation of strong VARMA processes. The asymptotic properties of this estimator are the same, than the relevant non-linear estimator.

We also propose an information criterion that generalizes the one proposed by Hannan and Rissanen (1982) and give consistent estimates of the order of the VARMA model. The VARMA representation used is the final equation form, but most of our results would still be valid for other representations.

Monte Carlo simulations are performed to illustrate the behavior of our estimation method. An application to several macroeconomics time series where we compute impulse response functions with a VARMA model is also presented.