Hostname: page-component-6898cfcb55-kwdml Total loading time: 0 Render date: 2026-11-11T11:01:31.132Z Has data issue: false hasContentIssue false
  • English
  • Français

Priors For The Ar(1) Model: Parameterization Issues and Time Series Considerations

Published online by Cambridge University Press:  11 February 2009

Peter C. Schotman
Peter C. Schotman
Affiliation:
University of Limburg
Get accessRights & Permissions [Opens in a new window]

Abstract

Two issues have come up in the specification of a prior in the Bayesian analysis of time series with possible unit roots. The first issue deals with the singularity that is due to the local identification problem of the unconditional mean of an AR(1) process in the limit of a random walk. This singularity problem is related to the difference between a structural parameterization and the linear reduced form in a standard regression model with fixed regressors. The second is related to the time series nature of the regressor in an AR(1) model. In this paper we will concentrate on the parameterization issue. First, it is shown that the posterior of the autoregressive parameter can be very sensitive to the degree of prior dependence between the unconditional mean and the autocorrelation parameter. Second, the time series nature of the problem suggests a particular form of this dependence.

Information

Type
Articles
Information
Econometric Theory , Volume 10 , Issue 3-4 , August 1994, pp. 579 - 595
Copyright
Copyright © Cambridge University Press 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCE

1.DeJong, D.N. & Whiteman, C.H.. The temporal stability of dividends and stock prices: Evidence from the likelihood function. American Economic Review 81 (1991): 600–617.Google Scholar
2.Phillips, P.C.B.To criticise the critics: An objective Bayesian analysis of stochastic trends. Journal of Applied Econometrics 6 (1991): 333–364.Google Scholar
3.Phillips, P.C.B.Bayesian routes and unit roots: De rebus prioribus semper est disputandum. Journal of Applied Econometrics 6 (1991): 435–473.Google Scholar
4.Schotman, P.C. & van Dijk, H.K.. A Bayesian analysis of the unit root in real exchange rates. Journal of Econometrics 49 (1991): 195–238.Google Scholar
5.Schotman, P.C. & van Dijk, H.K.. On Bayesian routes to unit roots. Journal of Applied Econometrics 6 (1991): 387–401.Google Scholar
6.Schotman, P.C. & van Dijk, H.K.. Posterior analysis of possibly integrated time series with an application to real GNP. In Caines, P., Geweke, J. & Taqqu, M. (eds.), New Directions in Time Series Analysis, Part II, pp. 341–362Berlin: Springer-Verlag, 1992.Google Scholar
7.Sims, C.A.Bayesian skepticism on unit root econometries. Journal of Economic Dynamics and Control 12 (1988): 463–474.Google Scholar
8.Tierney, L., Kass, R.E. & Kadane, J.B.. Approximate marginal densities of nonlinear functions. Biometrika 76 (1989): 425–433.Google Scholar
9.Uhlig, H.What macroeconomists should know about unit roots: The Bayesian perspective. Econometric Theory 10 (1994): 645–671.Google Scholar
10.Uhlig, H.On Jeffreys prior when using the exact likelihood function. Econometric Theory 10 (1994): 633–644.Google Scholar
11.Zellner, A.An Introduction to Bayesian Inference in Econometrics. New York: Wiley, 1971.Google Scholar
12.Zellner, A. Maximal data information prior distributions. In Aykac, A. & Brumat, C. (eds.), New Developments in the Applications of Bayesian Methods, pp. 211–232Amsterdam: North Holland, 1977.Google Scholar
13.Zellner, A.Estimation of functions of population means and regression coefficients including structural coefficients: A minimum expected loss (MELO) approach. Journal of Econometrics 8 (1978): 127–158.Google Scholar
14.Zivot, E.A Bayesian analysis of the unit root hypothesis within an unobserved components model. Econometric Theory 10 (1994): 552–578.Google Scholar