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Efficient Bayesian Inference for Multiple Change-Point and Mixture Innovation Models

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  • Giordani, Paolo

    ()
    (Research Department, Central Bank of Sweden)

  • Kohn, Robert

    (School of Economics, School of Banking and Finance)

Abstract

Time series subject to parameter shifts of random magnitude and timing are commonly modeled with a change-point approach using Chib's (1998) algorithm to draw the break dates. We outline some advantages of an alternative approach in which breaks come through mixture distributions in state innovations, and for which the sampler of Gerlach, Carter and Kohn (2000) allows reliable and efficient inference. We show how this approach can be used to (i) model shifts in variance that occur independently of shifts in other parameters (ii) draw the break dates efficiently in change-point and regime-switching models with either Markov or non-Markov transition probabilities. We extend the proofs given in Carter and Kohn (1994) and in Gerlach, Carter and Kohn (2000) to state-space models with system matrices which are functions of lags of the dependent variables, and we further improve the algorithms in Gerlach, Carter and Kohn by introducing to the time series literature the concept of adaptive Metropolis-Hastings sampling for discrete latent variable models. We develop an easily implemented adative algorithm that promises to sizably reduce computing time in a variety of problems including mixture innovation, change-point, regime-switching, and outlier detection.

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Bibliographic Info

Paper provided by Sveriges Riksbank (Central Bank of Sweden) in its series Working Paper Series with number 196.

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Length: 39 pages
Date of creation: 01 May 2006
Date of revision:
Handle: RePEc:hhs:rbnkwp:0196

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Postal: Sveriges Riksbank, SE-103 37 Stockholm, Sweden
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Related research

Keywords: Structural breaks; Parameter instability; Change-point; State-space; Mixtures; Discrete latent variables; Adaptive Metropolis-Hastings;

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References

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  1. Stock, James H & Watson, Mark W, 1996. "Evidence on Structural Instability in Macroeconomic Time Series Relations," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 14(1), pages 11-30, January.
  2. Gary Koop & Simon M. Potter, 2007. "Prior Elicitation in Multiple Change-point Models," Working Paper Series, The Rimini Centre for Economic Analysis 17-07, The Rimini Centre for Economic Analysis, revised Jul 2007.
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  9. Gary M. Koop & Simon M. Potter, 2004. "Forecasting and Estimating Multiple Change-point Models with an Unknown Number of Change-points," Discussion Papers in Economics, Department of Economics, University of Leicester 04/31, Department of Economics, University of Leicester.
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  14. Giordani, Paolo & Soderlind, Paul, 2003. "Inflation forecast uncertainty," European Economic Review, Elsevier, Elsevier, vol. 47(6), pages 1037-1059, December.
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  16. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, Econometric Society, vol. 66(1), pages 47-78, January.
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