Title: Reduced rank regression in a large VAR model
Authors: Kelly Trinh - University of Queensland (Australia) [presenting]
Rodney Strachan - The University of Queensland (Australia)
Abstract: The aim is to address the over-parameterization issue in large vector autoregressive (VAR) models by using reduced rank regression. A model specification will be provided which is invariant to the variable ordering. To select the rank of VAR coefficients, we consider a marginal likelihood approach which is approximated by cross entropy, predictive likelihood, and Laplace approximation. We carry out an extensive Monte Carlo simulation to examine the performance of these approaches in rank selection. The results suggest that these approaches underestimate the rank of VAR coefficients when the dimensions of VAR systems grow, and when the singular values of the VAR matrices are small (close to zero). We go further to examine the forecast performance of the misspecified rank models relative to the model with the correct rank (the benchmark model) using the measures of point forecast (e.g., mean squared forecast error, weighted mean squared forecast error) and density forecast (e.g., log predictive likelihood). Our results suggest that the models with lower rank perform worse than the benchmark for short forecast horizons, however, they perform as well as or even beat the benchmark for long forecast horizons. These patterns are more evident when the magnitudes of the singular values of the VAR coefficient are small.