Forecasts in a Slightly Misspecified Finite Order VAR
We propose a Bayesian procedure for exploiting small, possibly long-lag linear predictability in the innovations of a finite order autoregression. We model the innovations as having a log-spectral density that is a continuous mean-zero Gaussian process of order 1/√T. This local embedding makes the problem asymptotically a normal-normal Bayes problem, resulting in closed-form solutions for the best forecast. When applied to data on 132 U.S. monthly macroeconomic time series, the method is found to improve upon autoregressive forecasts by an amount consistent with the theoretical and Monte Carlo calculations.
This research was funded in part by NSF grant SBR-0617811 (Stock). We thank participants of workshops at Columbia, Harvard, and Montreal, and at the Greater New York Econometrics Colloquium for helpful comments, and Adam Clark-Joseph for excellent research assistance. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.