Orbital Priors for Time-Series Models
AbstractWe propose the unified approach to construct the non–informative prior for time–series econometric models that are invariant under some group of transformations. We show that this invariance property characterizes some of the most popular models hence the applicability of the proposed framework is quite general. The suggested prior enjoys many desirable properties both from the Bayesian and non–Bayesian perspective. We provide detailed derivations of our prior in many standard time–series models including, AutoRegressions (AR), Vector AutoRegressions (VAR), Structural VAR and Error Correction Models (ECM).
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 42804.
Date of creation: 23 Nov 2012
Date of revision:
Bayesian; Model invariance; Groups; Free group action; Orbit; Right Haar measure; Orbital decomposition; Maximal invariant; Cross section; Intersubjective prior; Vector AutoRegression (VAR); Structural VAR; Error Correction Model (ECM);
Find related papers by JEL classification:
- C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
- C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-12-10 (All new papers)
- NEP-ECM-2012-12-10 (Econometrics)
- NEP-ETS-2012-12-10 (Econometric Time Series)
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.:
- Zha, Tao, 1999. "Block recursion and structural vector autoregressions," Journal of Econometrics, Elsevier, vol. 90(2), pages 291-316, June.
- Christopher A. Sims & Tao Zha, 1996.
"Bayesian methods for dynamic multivariate models,"
96-13, Federal Reserve Bank of Atlanta.
- Chao, J. C. & Phillips, P. C. B., 1998. "Posterior distributions in limited information analysis of the simultaneous equations model using the Jeffreys prior," Journal of Econometrics, Elsevier, vol. 87(1), pages 49-86, August.
- Peter C.B. Phillips, 1990.
"To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends,"
Cowles Foundation Discussion Papers
950, Cowles Foundation for Research in Economics, Yale University.
- 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..
- Waggoner, Daniel F. & Zha, Tao, 2003.
"Likelihood preserving normalization in multiple equation models,"
Journal of Econometrics,
Elsevier, vol. 114(2), pages 329-347, June.
- Daniel F. Waggoner & Tao Zha, 2000. "Likelihood-preserving normalization in multiple equation models," Working Paper 2000-8, Federal Reserve Bank of Atlanta.
- Villani, Mattias, 2005. "Bayesian Reference Analysis Of Cointegration," Econometric Theory, Cambridge University Press, vol. 21(02), pages 326-357, April.
- 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.
- Schotman, Peter & van Dijk, Herman K., 1991. "A Bayesian analysis of the unit root in real exchange rates," Journal of Econometrics, Elsevier, vol. 49(1-2), pages 195-238.
- 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.
- Ni, Shawn & Sun, Dongchu, 2003. "Noninformative priors and frequentist risks of bayesian estimators of vector-autoregressive models," Journal of Econometrics, Elsevier, vol. 115(1), pages 159-197, July.
- Litterman, Robert B, 1986.
"Forecasting with Bayesian Vector Autoregressions-Five Years of Experience,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 4(1), pages 25-38, January.
- Robert B. Litterman, 1985. "Forecasting with Bayesian vector autoregressions five years of experience," Working Papers 274, Federal Reserve Bank of Minneapolis.
- Strachan, Rodney W. & Inder, Brett, 2004. "Bayesian analysis of the error correction model," Journal of Econometrics, Elsevier, vol. 123(2), pages 307-325, December.
- G. Datta & J. Ghosh, 1995. "Noninformative priors for maximal invariant parameter in group models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 4(1), pages 95-114, June.
- Gary Chamberlain & Marcelo J. Moreira, 2009. "Decision Theory Applied to a Linear Panel Data Model," Econometrica, Econometric Society, vol. 77(1), pages 107-133, 01.
- Gary Koop & Rodney Strachan & Herman van Dijk & Mattias Villani, 2004.
"Bayesian Approaches to Cointegration,"
Discussion Papers in Economics
04/27, Department of Economics, University of Leicester.
- Zivot, Eric, 1994. "A Bayesian Analysis Of The Unit Root Hypothesis Within An Unobserved Components Model," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 552-578, August.
- James Zidek, 1969. "A representation of Bayes invariant procedures in terms of Haar measure," Annals of the Institute of Statistical Mathematics, Springer, vol. 21(1), pages 291-308, December.
- Christopher A. Sims, 1988.
"Bayesian skepticism on unit root econometrics,"
Discussion Paper / Institute for Empirical Macroeconomics
3, Federal Reserve Bank of Minneapolis.
- Tom Doan, . "BAYESTST: RATS procedure to perform Bayesian Unit Root test," Statistical Software Components RTS00014, Boston College Department of Economics.
- 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.
- Mattias Villani, 2009. "Steady-state priors for vector autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(4), pages 630-650.
- Shawn Ni & Dongchu Sun, 2005. "Bayesian Estimates for Vector Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 105-117, January.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht).
If references are entirely missing, you can add them using this form.