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Marginal likelihood calculation for gelfand-dey and Chib Method

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  • Liu, Chun
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Abstract

One advantage of Bayesian estimation is its solid theoretical ground on model comparison, which relies heavily upon the accurate calculation of marginal likelihood. The Gelfand-Dey (1994) and Chib (1995) methods are two popular means of calculating marginal likelihood. A trade-off exists between these two methods. The Gelfand-Dey method is simpler and faster to conduct, while Chib method is more accurate, yet intricate. In this paper, we compare the two methods by their ability to identify structural breaks in a reduced form volatility model. Using the Markov Chain Monte Carlo method, we demonstrate that the performance of the two methods is fairly close. Since the Chib method is normally more di±cult to implement in many econometric problems, it is safe to choose Gelfand-Dey method when calculating marginal likelihood.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 34928.

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Date of creation: Oct 2010
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Handle: RePEc:pra:mprapa:34928

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Keywords: Model Comparison; Structural Break; Heterogeneous Autoregressive Model; Bayesain Estimation;

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  1. John Geweke, 1999. "Using simulation methods for bayesian econometric models: inference, development,and communication," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 18(1), pages 1-73.
  2. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 7(2), pages 174-196, Spring.
  3. G. M. Martin & C. S. Forbes, 1999. "Using simulation methods for bayesian econometric models: inference, development and communication: some comments," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 18(1), pages 113-118.
  4. Chun Liu & John M Maheu, 2007. "Are there Structural Breaks in Realized Volatility?," Working Papers, University of Toronto, Department of Economics tecipa-304, University of Toronto, Department of Economics.
  5. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2007. "Roughing It Up: Including Jump Components in the Measurement, Modeling and Forecasting of Return Volatility," CREATES Research Papers 2007-18, School of Economics and Management, University of Aarhus.
  6. W. E. Griffiths, 1999. "Estimating consumer surplus comments on "using simulation methods for bayesian econometric models: inference development and communication"," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 18(1), pages 75-87.
  7. Chib, Siddhartha, 1998. "Estimation and comparison of multiple change-point models," Journal of Econometrics, Elsevier, Elsevier, vol. 86(2), pages 221-241, June.
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