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Forecasting and estimating multiple change-point models with an unknown number of change points

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  • Gary M. Koop
  • Simon M. Potter

Abstract

This paper develops a new approach to change-point modeling that allows for an unknown number of change points in the observed sample. Our model assumes that regime durations have a Poisson distribution. The model approximately nests the two most common approaches: the time-varying parameter model with a change point every period and the change-point model with a small number of regimes. We focus on the construction of reasonable hierarchical priors both for regime durations and for the parameters that characterize each regime. A Markov Chain Monte Carlo posterior sampler is constructed to estimate a change-point model for conditional means and variances. We find that our techniques work well in an empirical exercise involving U.S. inflation and GDP growth. Empirical results suggest that the number of change points is larger than previously estimated in these series and the implied model is similar to a time-varying parameter model with stochastic volatility.

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Bibliographic Info

Paper provided by Federal Reserve Bank of New York in its series Staff Reports with number 196.

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Date of creation: 2004
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Handle: RePEc:fip:fednsr:196

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Keywords: Econometric models ; Time-series analysis;

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References

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  1. Lubos Pastor & Robert F. Stambaugh, 2000. "The Equity Premium and Structural Breaks," NBER Working Papers 7778, National Bureau of Economic Research, Inc.
  2. James H. Stock & Mark W. Watson, 1994. "Evidence on Structural Instability in Macroeconomic Time Series Relations," NBER Technical Working Papers 0164, National Bureau of Economic Research, Inc.
  3. 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, December.
  4. Timothy Cogley & Thomas Sargent, . "Evolving Post-World War II U.S. Inflation Dynamics," Working Papers 2132872, Department of Economics, W. P. Carey School of Business, Arizona State University.
  5. M. Hashem Pesaran & Davide Pettenuzzo & Allan Timmermann, 2006. "Forecasting Time Series Subject to Multiple Structural Breaks," Review of Economic Studies, Oxford University Press, vol. 73(4), pages 1057-1084.
  6. Perron, P. & Bai, J., 1995. "Estimating and Testing Linear Models with Multiple Structural Changes," Cahiers de recherche 9552, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  7. Gary Koop & Simon M. Potter, 1999. "Are apparent findings of nonlinearity due to structural instability in economic time series?," Staff Reports 59, Federal Reserve Bank of New York.
  8. John M. Maheu & Stephen Gordon, 2004. "Learning, Forecasting and Structural Breaks," Cahiers de recherche 0422, CIRPEE.
  9. Chib, Siddhartha, 1998. "Estimation and comparison of multiple change-point models," Journal of Econometrics, Elsevier, vol. 86(2), pages 221-241, June.
  10. Chopin, Nicolas & Pelgrin, Florian, 2004. "Bayesian inference and state number determination for hidden Markov models: an application to the information content of the yield curve about inflation," Journal of Econometrics, Elsevier, vol. 123(2), pages 327-344, December.
  11. Ang, Andrew & Bekaert, Geert, 2002. "Regime Switches in Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 163-82, April.
  12. Fernandez, Carmen & Osiewalski, Jacek & Steel, Mark F. J., 1997. "On the use of panel data in stochastic frontier models with improper priors," Journal of Econometrics, Elsevier, vol. 79(1), pages 169-193, July.
  13. Gary Koop & Simon M. Potter, 2004. "Prior Elicitation in Multiple Change-point Models," Discussion Papers in Economics 04/26, Department of Economics, University of Leicester.
  14. Sangjoon Kim, Neil Shephard & Siddhartha Chib, . "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers W26, revised version of W, Economics Group, Nuffield College, University of Oxford.
  15. Timothy Cogley & Thomas J. Sargent, 2003. "Drifts and volatilities: monetary policies and outcomes in the post WWII U.S," Working Paper 2003-25, Federal Reserve Bank of Atlanta.
  16. Chib, Siddhartha, 1996. "Calculating posterior distributions and modal estimates in Markov mixture models," Journal of Econometrics, Elsevier, vol. 75(1), pages 79-97, November.
  17. Olivier Blanchard & John Simon, 2001. "The Long and Large Decline in U.S. Output Volatility," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 32(1), pages 135-174.
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Cited by:
  1. Pesaran, Mohammad Hashem & Pettenuzzo, Davide & Timmermann, Allan, 2006. "Learning, structural instability and present value calculations," Discussion Paper Series 1: Economic Studies 2006,27, Deutsche Bundesbank, Research Centre.
  2. Jaehee Kim & Sooyoung Cheon, 2010. "Bayesian multiple change-point estimation with annealing stochastic approximation Monte Carlo," Computational Statistics, Springer, vol. 25(2), pages 215-239, June.
  3. John Geweke & Joel Horowitz & M. Hashem Pesaran, 2006. "Econometrics: A Bird’s Eye View," CESifo Working Paper Series 1870, CESifo Group Munich.
  4. Todd E. Clark & Michael W. McCracken, 2007. "Averaging forecasts from VARs with uncertain instabilities," Finance and Economics Discussion Series 2007-42, Board of Governors of the Federal Reserve System (U.S.).
  5. Ravazzolo, F. & van Dijk, D.J.C. & Paap, R. & Franses, Ph.H.B.F., 2006. "Bayesian Model Averaging in the Presence of Structural Breaks," Econometric Institute Research Papers EI 2006-33, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  6. Gary M. Koop & Simon M. Potter, 2004. "Prior elicitation in multiple change-point models," Staff Reports 197, Federal Reserve Bank of New York.
  7. Giordani, Paolo & Kohn, Robert, 2006. "Efficient Bayesian Inference for Multiple Change-Point and Mixture Innovation Models," Working Paper Series 196, Sveriges Riksbank (Central Bank of Sweden).
  8. Petros Dellaportas & David G. T. Denison & Chris Holmes, 2007. "Flexible Threshold Models for Modelling Interest Rate Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 419-437.

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