Practical methods for modelling weak VARMA processes: identification, estimation and specification with a macroeconomic application

Department of Economics, McGill University, H3A 2T7, Montréal, Québec, Canada

ABSTRACT program on Mathematics of Information Technology and Complex Systems (MITACS)], the Canada Council for the Arts (Killam Fellowship), the CIREQ, the CIRANO, and the Fonds FCAR (Government of Québec). William Dow Professor of Economics, McGill University, Centre interuniversitaire de recherche en analyse des organisations (CIRANO), and Centre interuniversitaire de recherche en économie quantitative (CIREQ). Mailing address: ABSTRACT In this paper, we develop practical methods for modelling weak VARMA processes. In a first part, we propose new identified VARMA representations, the diagonal MA equation form and the final MA equation form, where the MA operator is diagonal and scalar respectively. Both of these representations have the important feature that they constitute relatively simple modifications of a VAR model (in contrast with the echelon representation). In a second part, we study the problem of estimating VARMA models by relatively simple methods which only require linear regressions. We consider a generalization of the regression-based estimation method proposed by Hannan and Rissanen (1982). The asymptotic properties of the estimator are derived under weak hypotheses on the innovations (uncorrelated and strong mixing) so as to broaden the class of models to which it can be applied. In a third part, we present a modified information criterion which gives consistent estimates of the orders under the proposed representations. To demonstrate the importance of using VARMA models to study multivariate time series we compare the impulse-response functions and the out-of-sample forecasts generated by VARMA and VAR models.

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Available from: Jean-Marie Dufour, Dec 16, 2013
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    ABSTRACT: This article considers the problem of order selection of the vector autoregressive moving‐average (VARMA) models under the assumption that the errors are uncorrelated but not necessarily independent. These models are called weak VARMA by opposition to the standard VARMA models, also called strong VARMA models, in which the error terms are supposed to be i.i.d. We relax the standard independence assumption to extend the range of application of the VARMA models, allowing us to treat linear representations of general nonlinear processes. We propose a modified version of the Akaike information criterion for identifying the orders of weak VARMA models.
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