A1213
Title: Singular vector autoregressions
Authors: Eric Eisenstat - University of Queensland (Australia) [presenting]
Rodney Strachan - The University of Queensland (Australia)
Abstract: Methods are developed for multivariate time series that are assumed to have a strictly singular spectral density. This assumption is widely consistent with economic theory such as in Dynamic Stochastic General Equilibrium (DSGE) models, where the number of variables is almost always greater than the number of structural shocks. Empirically, this assumption guarantees the existence of a finite order VAR representation under mild regularity conditions. However, in this case, there does not exist a unique probability density function with respect to the Lebesgue measure. We overcome this difficulty by defining a density on a compact submanifold with respect to the Hausdorff measure instead. Accordingly, we develop an HMC algorithm that jointly samples model parameters, the VAR lag length, as well as the number of structural shocks in a fully specified Bayesian framework. The effectiveness of the methodology is demonstrated in an extensive Monte Carlo exercise involving a multi-sector DSGE model. Finally, we use the proposed framework to carry out structural analysis on US macroeconomic data in a sample involving COVID shocks.
