Multivariate Least Squares Forecasting Averaging by Vector Autoregressive Models
Author | : Jen-Che Liao |
Publisher | : |
Total Pages | : 47 |
Release | : 2016 |
Genre | : |
ISBN | : |
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This paper proposes a multivariate least squares Mallows averaging approach to the issue of forecast combination by vector autoregressive (VAR) model fitting. Our approach extends the current literature on frequentist least squares model/forecast averaging methods, in particular Hansen (2008), to multivariate time series models. We provide a theoretical foundation of our approach by presenting the relation between the proposed multivariate Mallows averaging criterion and the in-sample mean squared error and out-of-sample mean squared forecast error. We also establish the asymptotic properties such as unbiasedness and optimality of our approach. In a simulation experiment, the proposed approach performs well in finite samples relative to other selection and averaging methods. For an empirical illustration, we apply our methodology to forecasting U.S. macroeconomic dynamic systems based on small-scale and medium-scale VARs fitted to the datasets that were previously studied by Sims (1980) and Stock and Watson (2009).