Vector Autoregressions with Dynamic Factor Coefficients and Conditionally Heteroskedastic Errors

Abstract

We introduce a new and general methodology for analyzing vector autoregressive models with time-varying coefficient matrices and conditionally heteroskedastic disturbances. Our proposed method is able to jointly treat a dynamic latent factor model for the autoregressive coefficient matrices and a multivariate dynamic volatility model for the variance matrix of the disturbance vector. Since the likelihood function is available in closed-form through a simple extension of the Kalman filter equations, all unknown parameters in this flexible model can be easily estimated by the method of maximum likelihood. The proposed approach is appealing since it is simple to implement and computationally fast. Furthermore, it presents an alternative to Bayesian methods which are regularly employed in the empirical literature. A simulation study shows the reliability and robustness of the method against potential misspecifications of the volatility in the disturbance vector. We further provide an empirical illustration in which we analyze possibly time-varying relationships between U.S. industrial production, inflation, and bond spread. We empirically identify a time-varying linkage between economic and financial variables which are effectively described by a common dynamic factor. The impulse response analysis points towards substantial differences in the effects of financial shocks on output and inflation during crisis and non-crisis periods.

Keywords: time-varying parametersvector autoregressive model, dynamic factor model, Kalman filter, generalized autoregressive conditional heteroskedasticity, orthogonal impulse response function

JEL Classification: C32, E31