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Bayesian Analysis of ARMA Models using Noninformative Priors

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  • Frank Kleibergen

    ()
    (Erasmus University Rotterdam)

  • Henk Hoek

    (Erasmus University Rotterdam)

Abstract

Parameters in AutoRegressive Moving Average (ARMA) models are locally nonidentified, due to the problem of root cancellation. Parameters can be constructed which represent this identification problem. We argue that ARMA parameters should be analyzed conditional on these identifying parameters.Priors exploiting this feature result in regular posteriors, while priors which neglect it result in posteriori favor of nonidentified parameter values. By considering the implicit AR representation of an ARMA model a prior with the desired proporties is obtained. The implicit AR representation also allows to construct easily implemented algorithms to analyse ARMA parameters. As a byproduct, posteriors odds ratios can be computed to compare (nonnested) parsimonious ARMA models. The procedures are applied to two datasets, the (extended) Nelson-Plosser data and monthly observations of US 3-month and 10 year interest rates. For approximately 50% of the series in these two datasets an ARMA model is favored above an AR model.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 97-006/4.

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Date of creation: 21 Jan 1997
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Handle: RePEc:dgr:uvatin:19970006

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  1. Kleibergen, Frank & van Dijk, Herman K., 1994. "Direct cointegration testing in error correction models," Journal of Econometrics, Elsevier, vol. 63(1), pages 61-103, July.
  2. Franses, Philip Hans & Kleibergen, Frank, 1996. "Unit roots in the Nelson-Plosser data: Do they matter for forecasting?," International Journal of Forecasting, Elsevier, vol. 12(2), pages 283-288, June.
  3. Uhlig, Harald, 1994. "On Jeffreys Prior when Using the Exact Likelihood Function," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 633-644, August.
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  7. Kleibergen, Frank & van Dijk, Herman K., 1994. "On the Shape of the Likelihood/Posterior in Cointegration Models," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 514-551, August.
  8. Geweke, John, 1989. "Exact predictive densities for linear models with arch disturbances," Journal of Econometrics, Elsevier, vol. 40(1), pages 63-86, January.
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  14. Schotman, Peter C., 1994. "Priors For The Ar(1) Model: Parameterization Issues and Time Series Considerations," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 579-595, August.
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  16. DeJong, David N & Whiteman, Charles H, 1993. "Estimating Moving Average Parameters: Classical Pileups and Bayesian Posteriors," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(3), pages 311-17, July.
  17. Peter C.B. Phillips, 1987. "Partially Identified Econometric Models," Cowles Foundation Discussion Papers 845R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1988.
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