Publication Type
Journal Article
Version
submittedVersion
Publication Date
10-2018
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 vector of summary statistics of the original data. We establish 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.
Keywords
Bayesian average, Conditional mean estimation, Ergodic theorem, Summary statistic
Discipline
Econometrics
Research Areas
Econometrics
Publication
Journal of Econometrics
Volume
206
Issue
2
First Page
359
Last Page
378
ISSN
0304-4076
Identifier
10.1016/j.jeconom.2018.06.006
Publisher
Elsevier: 24 months
Citation
CHENG, Tingting; GAO, Jiti; and PHILLIPS, Peter C. B..
A frequentist approach to Bayesian asymptotics. (2018). Journal of Econometrics. 206, (2), 359-378.
Available at: https://ink.library.smu.edu.sg/soe_research/2348
Copyright Owner and License
Authors
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Additional URL
https://doi.org/10.1016/j.jeconom.2018.06.006