Skip to main content
×
Home
    • Aa
    • Aa

On Jeffreys Prior when Using the Exact Likelihood Function

  • Harald Uhlig (a1)
Abstract

In this paper, we calculate Jeffreys prior for an AR(1) process with and without a constant and a time trend when using the exact likelihood function. We show how this prior can be calculated for the explosive region, even though the unconditional variance of the process is infinite. The calculations lend additional support to the Schotman-van Dijk [6] procedure for restricting the location and the variance of the time trend coefficient. The results show that flat priors are reasonable for the nonexplosive region in an AR(1) without a constant and a time trend where the variance is known and the initial observation is zero, i.e., for the special case studied by Sims and Uhlig [7]. Differences to a flat prior analysis remain in particular for nonzero initial observations, however. For the explosive region, the unconditional prior diverges as the root diverges, supporting findings by Phillips [4]. This paper thus provides a useful perspective as well as some reconciliation for the different stands taken in the literature about priors and Bayesian inference for potentially nonstationary time series.

Copyright
References
Hide All
1.DeJong D.N., Nankervis J.C., Savin N.E. & Whiteman C.H.. Integration versus trend stationarity in time series. Econometrica 60 (1992): 423433.
2.Geweke J. Priors for macroeconomic time series and their application. Econometric Theory 10 (1994): 609632.
3.Learner E.E. Specification Searches. New York: Wiley, 1978.
4.Phillips P.C.B. To criticize the critics: An objective Bayesian analysis of stochastic trends. Journal of Applied Econometrics 6 (1991): 333364.
5.Phillips P.C.B. Bayesian routes and unit roots: De rebus prioribus semper est disputandum. Journal of Applied Econometrics 6 (1991): 435474.
6.Schotman P.C. & van Dijk H.K.. On Bayesian routes to unit roots. Journal of Applied Econometrics 6 (1991): 387402.
7.Sims C.A. & Uhlig H.. Understanding unit rooters: A helicopter tour. Econometrica 59 (1991): 15911600.
8.Thornber H. Finite sample Monte Carlo studies: An autoregressive illustration. Journal of the American Statistical Association 62 (1967): 801818.
9.Uhlig H. What macroeconomists should know about unit roots: A Bayesian perspective. Econometric Theory 10 (1994): 645671.
10.Zellner A. An Introduction to Bayesian Inference in Econometrics. New York: Wiley, 1971.
11.Zivot E. A Bayesian analysis of the unit root hypothesis within an unobserved components model. Econometric Theory 10 (1994): 552578.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 5 *
Loading metrics...

Abstract views

Total abstract views: 85 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 21st October 2017. This data will be updated every 24 hours.