Dimension reduction in vector autoregressive models for macroeconomic applications

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The vector autoregressive (VAR) model is instrumental in analyzing multivariate time series applications. However, as the number of parameters grows with the dimension of the VAR response vector, dimension reduction techniques are often necessary to improve model efficiency. The envelope approach [Cook RD, Li B, Chiaromonte F. Envelope models for parsimonious and efficient multivariate linear regression. Stat Sin. 2010;927–960] is a novel technique that enhances estimation efficiency and prediction accuracy in multivariate analysis by incorporating dimension reduction. In this paper, we introduce a novel class of envelope VAR (EVAR) models featuring elliptically contoured and stochastic volatility error innovations, aimed at enhancing the analysis of macroeconomic applications. Moreover, the asymptotic properties of the EVAR models without Gaussian error innovations are established. The simulation experiments and empirical analysis using macroeconomic data from the Federal Reserve Economic Data (FRED) database, demonstrate that the envelope VAR models with these error innovations outperform the standard VAR (OLSVAR) models in both estimation efficiency and forecast accuracy, especially when the data includes irrelevant or immaterial information.