Usage of Different Prior Distributions in Bayesian Vector Autoregressive Models

Abstract

Usage of Different Prior Distributions in Bayesian Vector Autoregressive Models

Abstract

In Bayesian vector autoregressive models, the Litterman or Minnesota Prior is widely used. However, in some cases, the Minnesota prior is not the best prior distribution that can be used. Thus, other prior distributions can also be applied. In this paper, as well as the Minnesota prior, four other prior distributions have been studied. Based on these prior distributions, five different Bayesian vector autoregressive models have been built to forecast the Turkish unemployment rate and the industrial production index for the two periods of the year 2008. Finally,
the five priors have been compared with each other according to the forecasting performances of the models that they are used in.

Keywords

• Bayesian vector autoregressive models,Vector autoregressive models,Prior Distributions,Bayes’ Theorem,Bayesian approach,2000 AMS Classification: 37 M 10

References

1. Berger, J. O. and Bernardo, J. M. On the development of reference priors, In: Bernardo, J.M. et al. (Bayesian Analysis IV, Oxford University Press, Oxford, 1992).
2. Bernardo, J. M., Reference posterior distributions for Bayesian, Inference, Journal of Royal Statistical Society Series B41, 113-147, 1979.
3. Canova, F. Methods for Applied Research 9 (Introduction to Bayesian Methods, Universitat Pompeu Fabra, 2004).
4. Dreze, J. H. and Morales, J. A. Bayesian full information analysis of simultaneous equations, Journal of the American Statistical Association 71, 919-23. Reprinted in A. Zellner, ed. Bayesian Analysis in Econometrics and Statistics (North-Holland, Amsterdam, 1980).
5. Dreze, J, H. and Richard, J. F. Bayesian analysis of simultaneous equation systems in Z. Griliches and M. D. Intrilligator eds. (Handbook of Econometrics, Vol. I, North-Holland, Amsterdam, 1980).
6. Efron, B. Why isn’t everyone a Bayesian?, American Statistician 40, 1-11, 1986.
7. Geisser, S. Bayesian estimation in multivariate analysis, Annals of Mathematical Statistics 36, 150-159, 1965.
8. Geweke, J. Antithetic acceleration of Monte Carlo integration in Bayesian inference, Jour nal of Econometrics 38, 73-89, 1988.

9. Kadiyala, K. R. and Karlsson, S. Numerical methods for estimation and inference in Bayesian VAR models, Journal of Applied Econometrics 12, 99-132, 1997.
10. Lindley, D.V. The Bayesian approach, Scandinavian Journal of Statistics 5, 1-26, 1978.
11. Litterman, R.B. A Bayesian Procedure for Forecasting with Vector Autoregressions (Mimeo, Massachussets Institute of Technology, 1980).
12. Litterman, R. B. Forecasting with Bayesian vector autoregressions - Five years of experience, Journal of Business and Economic Statistics 4, 25-38, 1986.
13. Sims, C.A. Macroeconomics and reality, Econometrica 48 (1), 1-48, 1980.
14. Tiao, G.C. and Zellner, A. On Bayesian estimation of multivariate regression, Journal of the Royal Statistical Society B26, 389-99, 1964.
15. Zellner, A. An Introduction to Bayesian Inference in Econometrics (John Wiley, New York, 1974).