IDEAS home Printed from https://ideas.repec.org/p/msh/ebswps/2016-5.html
   My bibliography  Save this paper

A Frequency Approach to Bayesian Asymptotics

Author

Listed:
  • Tingting Cheng

    ()

  • Jiti Gao

    ()

  • Peter CB Phillips

    ()

Abstract

Ergodic theorem shows that ergodic averages of the posterior draws converge in probability to the posterior mean under the stationarity assumption. The literature also shows that the posterior distribution is asymptotically normal when the sample size of the original data considered goes to infinity. To the best of our knowledge, there is little discussion on the large sample behaviour of the posterior mean. In this paper, we aim to fill this gap. In particular, we extend the posterior mean idea to the conditional mean case, which is conditioning on a given summary statistics of the original data. We stablish a new asymptotic theory for the conditional mean estimator for the case when both the sample size of the original data concerned and the number of Markov chain Monte Carlo iterations go to infinity. Simulation studies show that this conditional mean estimator has very good finite sample performance. In addition, we employ the conditional mean estimator to estimate a GARCH(1,1) model for S&P 500 stock returns and find that the conditional mean estimator performs better than quasi-maximum likelihood estimation in terms of out-of-sample forecasting.

Suggested Citation

  • 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.
  • Handle: RePEc:msh:ebswps:2016-5
    as

    Download full text from publisher

    File URL: http://business.monash.edu/econometrics-and-business-statistics/research/publications/ebs/wp05-16.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Phillips, Peter C B & Ploberger, Werner, 1996. "An Asymptotic Theory of Bayesian Inference for Time Series," Econometrica, Econometric Society, vol. 64(2), pages 381-412, March.
    2. 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.
    3. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Bayesian average; conditional mean estimation; ergodic theorem; summary statistic;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:msh:ebswps:2016-5. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dr Xibin Zhang) or (Joanne Lustig). General contact details of provider: http://edirc.repec.org/data/dxmonau.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.