Estimation and Forecasting in Vector Autoregressive Moving Average Models for Rich Datasets
40 Pages Posted: 23 Dec 2015 Last revised: 11 Jun 2021
Date Written: May 29, 2017
We address the issue of modelling and forecasting macroeconomic variables using rich datasets by adopting the class of Vector Autoregressive Moving Average (VARMA) models. We overcome the estimation issue that arises with this class of models by implementing an iterative ordinary least squares (IOLS) estimator. We establish the consistency and asymptotic distribution of the estimator for weak and strong VARMA(p,q) models. Monte Carlo results show that IOLS is consistent and feasible for large systems, outperforming the MLE and other linear regression based efficient estimators under alternative scenarios. Our empirical application shows that VARMA models are feasible alternatives when forecasting with many predictors. We show that VARMA models outperform the AR(1), ARMA(1,1), Bayesian VAR, and factor models, considering different model dimensions.
Supplement is available at: https://ssrn.com/abstract=2830838
Keywords: VARMA, weak VARMA, weak ARMA, Forecasting, Large datasets, Iterative ordinary least squares (IOLS) estimator, Asymptotic contraction mapping
JEL Classification: C13, C32, C53, C63, E0
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