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On Marginal Likelihood Computation in Change-point Models

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  • Luc Bauwens
  • Jeroen V.K. Rombouts

Abstract

Change-point models are useful for modeling times series subject to structural breaks. For interpretation and forecasting, it is essential to estimate correctly the number of change points in this class of models. In Bayesian inference, the number of change-points is typically chosen by the marginal likelihood criterion, computed by Chib’s method. This method requires to select a value in the parameter space at which the computation is done. We explain in detail how to perform Bayesian inference for a change point dynamic regression model and how to compute its marginal likelihood. Motivated by our results from three empirical illustrations, a simulation study shows that Chib’s method is robust with respect to the choice of the parameter value used in the computations, among posterior mean, mode and quartiles. Furthermore, the performance of the Bayesian information criterion, which is based on maximum likelihood estimates, in selecting the correct model is comparable to that of the marginal likelihood.

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Bibliographic Info

Paper provided by CIRPEE in its series Cahiers de recherche with number 0942.

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Date of creation: 2009
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Handle: RePEc:lvl:lacicr:0942

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Keywords: BIC; Change-point model; Chib's method; Marginal likelihood;

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References

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  1. Lubos Pástor & Robert F. Stambaugh, . "The Equity Premium and Structural Breaks," Rodney L. White Center for Financial Research Working Papers 21-98, Wharton School Rodney L. White Center for Financial Research.
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  12. Neil Shephard & Ola Elerian & Siddhartha Chib, 1998. "Likelihood inference for discretely observed non-linear diffusions," Economics Series Working Papers 1998-W10, University of Oxford, Department of Economics.
  13. Paroli, Roberta & Spezia, Luigi, 2008. "Bayesian inference in non-homogeneous Markov mixtures of periodic autoregressions with state-dependent exogenous variables," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2311-2330, January.
  14. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika van der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639.
  15. Kim, Chang-Jin & Morley, James C. & Nelson, Charles R., 2005. "The Structural Break in the Equity Premium," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 181-191, April.
  16. Frühwirth-Schnatter, Sylvia & Wagner, Helga, 2008. "Marginal likelihoods for non-Gaussian models using auxiliary mixture sampling," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4608-4624, June.
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  18. Chib, Siddhartha, 1998. "Estimation and comparison of multiple change-point models," Journal of Econometrics, Elsevier, vol. 86(2), pages 221-241, June.
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Cited by:
  1. Joshua C.C. Chan & Angelia L. Grant, 2014. "Fast Computation of the Deviance Information Criterion for Latent Variable Models," CAMA Working Papers 2014-09, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  2. van den Hout, Ardo & Muniz-Terrera, Graciela & Matthews, Fiona E., 2013. "Change point models for cognitive tests using semi-parametric maximum likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 684-698.

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