PC-VAR Estimation of Vector Autoregressive Models
Università di Milano Bicocca; Università degli Studi di Milano-Bicocca - Department of Economics, Quantitative Methods and Business Strategies (DEMS); Center for Economic Research on Pensions and Welfare Policies (CeRP); University of Bologna - Rimini Center for Economic Analysis (RCEA)
February 11, 2012
Open Journal of Statistics, 2012, 2, 251-259
In this paper PC-VAR estimation of vector autoregressive models (VAR) is proposed. The estimation strategy successfully lessen the curse of dimensionality affecting VAR models, when estimated using sample sizes typically available in quarterly studies. The procedure involves a dynamic regression using a subset of principal components extracted from a vector time series, and the recovery of the implied unrestricted VAR parameter estimates by solving a set of linear constraints. PC-VAR and OLS estimation of unrestricted VAR models show the same asymptotic properties. Monte Carlo results strongly support PC-VAR estimation, yielding gains, in terms of both lower bias and higher efficiency, relatively to OLS estimation of high dimensional unrestricted VAR models in small samples. Guidance for the selection of the number of components to be used in empirical studies is provided.
Keywords: vector autoregressive model, principal components analysis, statistical reduction techniques
JEL Classification: C22
Date posted: February 18, 2012 ; Last revised: June 9, 2013
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