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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. John M. Maheu & Stephen Gordon, 2004. "Learning, Forecasting and Structural Breaks," Cahiers de recherche 0422, CIRPEE.
  2. 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.
  3. 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.
  4. Timothy Cogley & Thomas Sargent, . "Drifts and Volatilities: Monetary Policies and Outcomes in the Post WWII US," Working Papers 2133503, Department of Economics, W. P. Carey School of Business, Arizona State University.
  5. 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.
  6. Pesaran, M Hashem & Pettenuzzo, Davide & Timmermann, Allan G, 2004. "Forecasting Time Series Subject to Multiple Structural Breaks," CEPR Discussion Papers 4636, C.E.P.R. Discussion Papers.
  7. 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.
  8. Andrew Ang & Geert Bekaert, 1998. "Regime Switches in Interest Rates," NBER Working Papers 6508, National Bureau of Economic Research, Inc.
  9. James H. Stock & Mark W. Watson, 1994. "Evidence on structural instability in macroeconomic times series relations," Working Paper Series, Macroeconomic Issues 94-13, Federal Reserve Bank of Chicago.
  10. Chib, Siddhartha, 1996. "Calculating posterior distributions and modal estimates in Markov mixture models," Journal of Econometrics, Elsevier, vol. 75(1), pages 79-97, November.
  11. 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.
  12. Kim, Sangjoon & Shephard, Neil & Chib, Siddhartha, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 361-93, July.
  13. Lubos Pastor & Robert F. Stambaugh, 2000. "The Equity Premium and Structural Breaks," NBER Working Papers 7778, National Bureau of Economic Research, Inc.
  14. 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.
  15. Chib, Siddhartha, 1998. "Estimation and comparison of multiple change-point models," Journal of Econometrics, Elsevier, vol. 86(2), pages 221-241, June.
  16. 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.
  17. 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.
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Citations

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Cited by:
  1. John Geweke & Joel Horowitz & M. Hashem Pesaran, 2006. "Econometrics: A Bird’s Eye View," CESifo Working Paper Series 1870, CESifo Group Munich.
  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. 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.).
  4. 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.
  5. Pesaran, M.H. & Pettenuzzo, D. & Timmermann, A., 2006. "Learning, Structural Instability and Present Value Calculations," Cambridge Working Papers in Economics 0602, Faculty of Economics, University of Cambridge.
  6. 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).
  7. 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.
  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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