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

  • Giordani, Paolo

    ()

    (Research Department, Central Bank of Sweden)

  • Kohn, Robert

    (School of Economics, School of Banking and Finance)

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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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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  1. David J. Nott & Robert Kohn, 2005. "Adaptive sampling for Bayesian variable selection," Biometrika, Biometrika Trust, vol. 92(4), pages 747-763, December.
  2. Stock, James H & Watson, Mark W, 1996. "Evidence on Structural Instability in Macroeconomic Time Series Relations," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 11-30, January.
  3. Gary Koop & Simon M. Potter, 2007. "Prior Elicitation in Multiple Change-point Models," Working Paper Series 17-07, The Rimini Centre for Economic Analysis, revised Jul 2007.
  4. M. Hashem Pesaran & Davide Pettenuzzo & Allan Timmermann, 2004. "Forecasting Time Series Subject to Multiple Structural Breaks," CESifo Working Paper Series 1237, CESifo Group Munich.
  5. George A. Akerlof & William T. Dickens & George L. Perry, 2000. "Near-Rational Wage and Price Setting and the Long-Run Phillips Curve," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 31(1), pages 1-60.
  6. Giordani, P. & Kohn, R. & van Dijk, D.J.C., 2005. "A unified approach to nonlinearity, structural change and outliers," Econometric Institute Research Papers EI 2005-09, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  7. Gary M. Koop & Simon M. Potter, 2004. "Forecasting and estimating multiple change-point models with an unknown number of change points," Staff Reports 196, Federal Reserve Bank of New York.
  8. Christopher A. Sims, 1992. "A Nine Variable Probabilistic Macroeconomic Forecasting Model," Cowles Foundation Discussion Papers 1034, Cowles Foundation for Research in Economics, Yale University.
  9. Söderlind, Paul, 2000. "Inflation Forecast Uncertainty," CEPR Discussion Papers 2499, C.E.P.R. Discussion Papers.
  10. Michael P. Clements & David F. Hendry, 2001. "Forecasting Non-Stationary Economic Time Series," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262531895, June.
  11. Sangjoon Kim & Neil Shephard, 1994. "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers 3., Economics Group, Nuffield College, University of Oxford.
  12. Chib, Siddhartha, 1998. "Estimation and comparison of multiple change-point models," Journal of Econometrics, Elsevier, vol. 86(2), pages 221-241, June.
  13. J Huston McCulloch, 2000. "State-Space Times Series Modeling of Structural Breaks," Working Papers 00-11, Ohio State University, Department of Economics.
  14. Lawrence J. Christiano & Terry J. Fitzgerald, 2003. "Inflation and monetary policy in the twentieth century," Economic Perspectives, Federal Reserve Bank of Chicago, issue Q I, pages 22-45.
  15. Thomas Sargent & Noah Williams & Tao Zha, 2009. "The Conquest of South American Inflation," Journal of Political Economy, University of Chicago Press, vol. 117(2), pages 211-256, 04.
  16. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
  17. Timothy Cogley & Thomas J. Sargent, 2002. "Evolving Post-World War II U.S. Inflation Dynamics," NBER Chapters, in: NBER Macroeconomics Annual 2001, Volume 16, pages 331-388 National Bureau of Economic Research, Inc.
  18. Bruce E. Hansen, 2001. "The New Econometrics of Structural Change: Dating Breaks in U.S. Labour Productivity," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 117-128, Fall.
  19. Carter, C.K. & Kohn, R., . "Semiparametric Bayesian inference for time series with mixed spectra," Statistics Working Paper _005, Australian Graduate School of Management.
  20. J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Biometrika Trust, vol. 89(3), pages 603-616, August.
  21. Schorfheide, Frank, 2000. "Forecasting Economic Time Series," Econometric Theory, Cambridge University Press, vol. 16(03), pages 441-450, June.
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