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Large Sample Properties of Posterior Densities, Bayesian Information Criterion and the Likelihood Principle in Nonstationary Time Series Models

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  • Jae-Young Kim

Abstract

Asymptotic normality of posterior is a well understood result for dynamic as well as non-dynamic models based on sets of abstract conditions that are hard to verify especially for the case of nonstationarity. In this paper the authors provide a set of conditions by which they can relatively easily prove the asymptotic posterior normality under quite general situations of possible nonstationarity. This result reinforces and generalizes the validity of inference based on the likelihood principle. On the other hand, the authors' conditions allow them to generalize Bayesian decision criterion to the case of possible nonstationarity. In addition, the authors have shown that consistency of the maximum likelihood estimator, not the asymptotic normality of the estimator, with some minor additional assumptions is sufficient for the asymptotic posterior normality.

Suggested Citation

  • Jae-Young Kim, 1998. "Large Sample Properties of Posterior Densities, Bayesian Information Criterion and the Likelihood Principle in Nonstationary Time Series Models," Econometrica, Econometric Society, vol. 66(2), pages 359-380, March.
  • Handle: RePEc:ecm:emetrp:v:66:y:1998:i:2:p:359-380
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    Cited by:

    1. Tingting Cheng & Jiti Gao & Xibin Zhang, 2015. "Bayesian Bandwidth Estimation In Nonparametric Time-Varying Coefficient Models," Monash Econometrics and Business Statistics Working Papers 3/15, Monash University, Department of Econometrics and Business Statistics.
    2. Mackowiak, Bartosz, 2006. "What does the Bank of Japan do to East Asia?," Journal of International Economics, Elsevier, vol. 70(1), pages 253-270, September.
    3. Chao, John C. & Phillips, Peter C. B., 1999. "Model selection in partially nonstationary vector autoregressive processes with reduced rank structure," Journal of Econometrics, Elsevier, vol. 91(2), pages 227-271, August.
    4. Hyungsik Roger Moon & Frank Schorfheide, 2012. "Bayesian and Frequentist Inference in Partially Identified Models," Econometrica, Econometric Society, vol. 80(2), pages 755-782, March.
    5. George Monokroussos, 2013. "A Classical MCMC Approach to the Estimation of Limited Dependent Variable Models of Time Series," Computational Economics, Springer;Society for Computational Economics, vol. 42(1), pages 71-105, June.
    6. Ana Beatriz Galvão & Liudas Giraitis & George Kapetanios & Katerina Petrova, 2015. "A Bayesian Local Likelihood Method for Modelling Parameter Time Variation in DSGE Models," Working Papers 770, Queen Mary University of London, School of Economics and Finance.
    7. Jesús Fernández-Villaverde, 2010. "The econometrics of DSGE models," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 1(1), pages 3-49, March.
    8. Ploberger, Werner & Phillips, Peter C.B., 2012. "Optimal estimation under nonstandard conditions," Journal of Econometrics, Elsevier, vol. 169(2), pages 258-265.
    9. Tingting Cheng & Jiti Gao & Peter CB Phillips, 2017. "Bayesian estimation based on summary statistics: Double asymptotics and practice," Monash Econometrics and Business Statistics Working Papers 4/17, Monash University, Department of Econometrics and Business Statistics.
    10. Fernandez-Villaverde, Jesus & Francisco Rubio-Ramirez, Juan, 2004. "Comparing dynamic equilibrium models to data: a Bayesian approach," Journal of Econometrics, Elsevier, vol. 123(1), pages 153-187, November.
    11. Bartosz Maćkowiak, 2006. "How Much of the Macroeconomic Variation in Eastern Europe is Attributable to External Shocks?," Comparative Economic Studies, Palgrave Macmillan;Association for Comparative Economic Studies, vol. 48(3), pages 523-544, September.
    12. Thomas A. Lubik & Frank Schorfheide, 2004. "Testing for Indeterminacy: An Application to U.S. Monetary Policy," American Economic Review, American Economic Association, vol. 94(1), pages 190-217, March.
    13. Peter C.B. Phillips, 2008. "Unit Root Model Selection," Cowles Foundation Discussion Papers 1653, Cowles Foundation for Research in Economics, Yale University.
    14. Marriott, John & Newbold, Paul, 2000. "The strength of evidence for unit autoregressive roots and structural breaks: A Bayesian perspective," Journal of Econometrics, Elsevier, vol. 98(1), pages 1-25, September.
    15. Thomas Lubik & Frank Schorfheide, 2002. "Testing for Indeterminacy in Linear Rational Expectations Models," Computing in Economics and Finance 2002 214, Society for Computational Economics.
    16. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 113-172.
    17. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    18. Penelope Smith, 2006. "Bayesian Inference for a Threshold Autoregression with a Unit Root," Melbourne Institute Working Paper Series wp2006n20, Melbourne Institute of Applied Economic and Social Research, The University of Melbourne.
    19. Tingting Cheng & Jiti Gao & Peter CB Phillips, 2016. "A Frequency Approach to Bayesian Asymptotics," Monash Econometrics and Business Statistics Working Papers 5/16, Monash University, Department of Econometrics and Business Statistics.
    20. Li, Yong & Zeng, Tao & Yu, Jun, 2014. "A new approach to Bayesian hypothesis testing," Journal of Econometrics, Elsevier, vol. 178(P3), pages 602-612.
    21. Lee, Namgil & Choi, Hyemi & Kim, Sung-Ho, 2016. "Bayes shrinkage estimation for high-dimensional VAR models with scale mixture of normal distributions for noise," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 250-276.
    22. Nikolay Iskrev, 2018. "Calibration and the estimation of macroeconomic models," Working Papers REM 2018/34, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.

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