Bayesian Analysis of ARMA Models using Noninformative Priors

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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)

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Frank Kleibergen

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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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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Paper
- Kleibergen, F. & Hoek, H., 1995. "Bayesian analysis of ARMA models using noninformative priors," Discussion Paper 116, Tilburg University, Center for Economic Research. [Downloadable!]
- Kleibergen, Frank & Hoek, Henk, 1996. "Bayesian analysis of ARMA models using noninformative priors," Econometric Institute Report 39, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
- Kleibergen, F.R. & Hoek, H., 1995. "Bayesian Analysis of ARMA models using Noninformative Priors," Econometric Institute Report EI 9553-/B Revision_Date:, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

Monahan, John F., 1983. "Fully Bayesian analysis of ARMA time series models," Journal of Econometrics, Elsevier, vol. 21(3), pages 307-331, April. [Downloadable!] (restricted)
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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. [Downloadable!]
Other versions:
- Kleibergen, F.R. & Van Dijk, H.K., 1993. "On the Shape of the Likelyhood/Posterior in Cointegration Models," Papers 9315-a, Erasmus University of Rotterdam - Econometric Institute.
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.
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Peter C.B. Phillips, 1987. "Partially Identified Econometric Models," Cowles Foundation Discussion Papers 845R, Cowles Foundation, Yale University, revised Aug 1988. [Downloadable!]
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. [Downloadable!] (restricted)
Other versions:
- Kleinbergen, F.R. & Van Dijk, H.K., 1993. "Direct Cointegration Testing in Error Correction Models," Papers 9334-a, Erasmus University of Rotterdam - Econometric Institute.
Phillips, P C B, 1991. "To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 333-64, Oct.-Dec.. [Downloadable!] (restricted)
Other versions:
- Peter C.B. Phillips, 1990. "To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends," Cowles Foundation Discussion Papers 950, Cowles Foundation, Yale University. [Downloadable!]
Geweke, John, 1989. "Exact predictive densities for linear models with arch disturbances," Journal of Econometrics, Elsevier, vol. 40(1), pages 63-86, January. [Downloadable!] (restricted)
Sargan, J D & Bhargava, Alok, 1983. "Maximum Likelihood Estimation of Regression Models with First Order Moving Average Errors When the Root Lies on the Unit Circle," Econometrica, Econometric Society, vol. 51(3), pages 799-820, May. [Downloadable!] (restricted)
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. [Downloadable!]
Schotman, Peter C & van Dijk, Herman K, 1991. "On Bayesian Routes to Unit Roots," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 387-401, Oct.-Dec.. [Downloadable!] (restricted)
Other versions:
- Peter C. Schotman & Herman K. van Dijk, 1991. "On Bayesian routes to unit roots," Discussion Paper / Institute for Empirical Macroeconomics 43, Federal Reserve Bank of Minneapolis. [Downloadable!]
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. [Downloadable!] (restricted)

Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

P. Saikkonen & H. Lütkepohl, . "Testing for a Unit Root in a Time Series with a Level Shift at Unknown Time," Sonderforschungsbereich 373 1999-72, Humboldt Universitaet Berlin.
Other versions:
- Helmut Luetkepohl & Pentti Saikkonen, 2000. "Testing for a Unit Root in a Time Series with a Level Shift at Unknown Time," Econometric Society World Congress 2000 Contributed Papers 0342, Econometric Society. [Downloadable!]
M. Lanne & H. Lütkepohl & P. Saikkonen, . "Test Procedures for Unit Roots in Time Series with Level Shifts at Unknown Time," Sonderforschungsbereich 373 2001-39, Humboldt Universitaet Berlin.
Other versions:
- Markku Lanne & Helmut Lutkepohl & Pentti Saikkonen, 2003. "Test Procedures for Unit Roots in Time Series with Level Shifts at Unknown Time," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(1), pages 91-115, February. [Downloadable!] (restricted)
Kleibergen, Frank & Dijk, Herman K. van, 1996. "Bayesian simultaneous equations analysis using reduced rank structures," Econometric Institute Report 47, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
Other versions:
- Kleibergen, F. & Van Dijk, H.K., 1997. "Bayesian Simultaneous Equations Analysis Using Reduced Rank Structures," Papers 9714/a, Erasmus University of Rotterdam - Econometric Institute.
- Kleibergen, F.R. & Dijk, H.K. van, 1997. "Bayesian Simultaneous Equations Analysis using Reduced Rank Structures," Econometric Institute Report EI 9714/A Revision_Date: , Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
- Kleibergen, Frank & van Dijk, Herman K., 1998. "Bayesian Simultaneous Equations Analysis Using Reduced Rank Structures," Econometric Theory, Cambridge University Press, vol. 14(06), pages 701-743, December. [Downloadable!]
Kleibergen, Frank & Paap, Richard, 1996. "Priors, posterior odds and Lagrange multiplier statistics in Bayesian analyses of cointegration," Econometric Institute Report 37, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
Other versions:
- Frank Kleibergen & Richard Paap, 1997. "Priors, Posterior Odds and Lagrange Multiplier Statistics in Bayesian Analyses of Cointegration," Tinbergen Institute Discussion Papers 97-007/4, Tinbergen Institute.
- Kleibergen, F.R. & Paap, R., 1996. "Priors, Posterior Odds and Lagrange Multiplier Statistics in Bayesian Analyses of Cointegration," Econometric Institute Report EI 9668-/A Revision_Date:, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]

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