Practical Methods for Modeling Weak VARMA Processes: Identification, Estimation and Specification With a Macroeconomic Application

Abstract

We consider the problem of developing practical methods for modelling weak VARMA processes. We first propose new identified VARMA representations, the diagonal MA equation form and the final MA equation form, where the MA operator is either diagonal or scalar. Both these representations have the important feature that they constitute relatively simple modifications of a VAR model (in contrast with the echelon representation). Second, for estimating VARMA models, we develop computationally simple methods which only require linear regressions. The asymptotic properties of the estimator are derived under weak hypotheses on the innovations (uncorrelated and strong mixing), in order to broaden the class of models to which it can be applied. Third, we present a modified information criterion which yields consistent estimates of the orders under the proposed representations. The estimation methods are studied by simulation. 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. The proposed methodology is applied to a six-variable macroeconomic model of monetary policy, based on the U.S. monthly data over the period 1962–1996. The results demonstrate the advantages of using the VARMA methodology for impulse response estimation and forecasting, in contrast with standard VAR models.