Daniel F. Waggoner and Tao Zha
Federal Reserve Bank of Atlanta
Working Paper 98-22
December 1998
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In the existing literature, conditional forecasts in the vector autoregressive (VAR) framework have not been commonly presented with probability distributions or error bands. This paper develops Bayesian methods for computing such distributions or bands. It broadens the class of conditional forecasts to which the methods can be applied. The methods work for both structural and reduced-form VAR models and, in contrast to common practices, account for the parameter uncertainty in small samples. Empirical examples under the flat prior and under the reference prior of Sims and Zha (1998) are provided to show the use of these methods.
JEL classification: C32, E17, C53
Key words: conditional forecasts, hard and soft conditions, Bayesian methods, probability distribution, error bands, likelihood
The authors thank seminar participants at the 1998 Midwest Econometric Group meetings, Queen's, UQAM, MSU, ISU, and Michigan; Frank Diebold; Bob Eisenbeis; Lutz Kilian; Eric Leeper; Will Roberds; Matt Shapiro; Ellis Tallman; especially John Robertson; Chris Sims; and Chuck Whiteman for valuable comments on earlier drafts. Bryan Acree and Jeff Johnson provided able research assistance. The views expressed here are those of the authors and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors' responsibility.
Please address questions regarding content to Daniel F. Waggoner, Senior Quantitative Analyst, Research Department, Federal Reserve Bank of Atlanta, 104 Marietta Street, NW, Atlanta, Georgia 30303-2713, 404/498-8278, 404/498-8810 (fax), daniel.f.waggoner@atl.frb.org; or Tao A. Zha, Senior Economist, Research Department, Federal Reserve Bank of Atlanta, 104 Marietta Street, NW, Atlanta, Georgia 30303-2713, 404/498-8353, 404/498-8956 (fax), tzha@ mindspring.com.