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A structural Time Series Model with Markov Switching

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  • Shami, R.G.
  • Forbes, C.S.

Abstract

We propose an innovations form of the structural model underlying exponential smoothing that is further augmented by a latent Markov switching process. A particular case of the new model is the local level model with a switching drift, where the switching component describes the change between high and low growth rate periods. This new model is used to analyse the US business cycle using US Quarterly real GNP data. Model parameters are estimated using a Gibbs sampling algorithm and subsequently used for forecasting purposes. In addition, the stability of the new model is tested against Hamilton's model over a range of observation periods.

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File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2000/wp10-00.pdf
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Bibliographic Info

Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 10/00.

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Length: 29 pages
Date of creation: Dec 2000
Date of revision:
Handle: RePEc:msh:ebswps:2000-10

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Keywords: Structural models; Markov switching regime; Gibbs sampling Business cycle.;

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References

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  1. Ord, J.K. & Koehler, A. & Snyder, R.D., 1995. "Estimation and Prediction for a Class of Dynamic Nonlinear Statistical Models," Monash Econometrics and Business Statistics Working Papers 4/95, Monash University, Department of Econometrics and Business Statistics.
  2. Perron, Pierre & Phillips, Peter C. B., 1987. "Does GNP have a unit root? : A re-evaluation," Economics Letters, Elsevier, vol. 23(2), pages 139-145.
  3. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, vol. 18(1), pages 49-75, July.
  4. Cecchetti, Stephen G & Lam, Pok-sang & Mark, Nelson C, 1990. "Mean Reversion in Equilibrium Asset Prices," American Economic Review, American Economic Association, vol. 80(3), pages 398-418, June.
  5. Hamilton, James D & Gang, Lin, 1996. "Stock Market Volatility and the Business Cycle," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(5), pages 573-93, Sept.-Oct.
  6. Aoki, Masanao, 1988. "On alternative state space representations of time series models," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 595-607.
  7. Albert, James H & Chib, Siddhartha, 1993. "Bayes Inference via Gibbs Sampling of Autoregressive Time Series Subject to Markov Mean and Variance Shifts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 1-15, January.
  8. Clark, Peter K, 1987. "The Cyclical Component of U.S. Economic Activity," The Quarterly Journal of Economics, MIT Press, vol. 102(4), pages 797-814, November.
  9. Harvey, A C, 1985. "Trends and Cycles in Macroeconomic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(3), pages 216-27, June.
  10. Hansen, Bruce E, 1992. "The Likelihood Ratio Test under Nonstandard Conditions: Testing the Markov Switching Model of GNP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages S61-82, Suppl. De.
  11. Forbes, C.S. & Snyder, R.D. & Shami, R.S., 2000. "Bayesian Exponential Smoothing," Monash Econometrics and Business Statistics Working Papers 7/00, Monash University, Department of Econometrics and Business Statistics.
  12. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
  13. Shami, R.G. & Snyder, R.D., 1998. "Exponential Smoothing Methods of Forecasting and General ARMA Time Series Representations," Monash Econometrics and Business Statistics Working Papers 3/98, Monash University, Department of Econometrics and Business Statistics.
  14. Francis X. Diebold & Glenn D. Rudebusch, 1987. "Scoring the leading indicators," Special Studies Papers 206, Board of Governors of the Federal Reserve System (U.S.).
  15. Kim, Chang-Jin, 1994. "Dynamic linear models with Markov-switching," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 1-22.
  16. Chang-Jin Kim & Charles R. Nelson, 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262112388, December.
  17. Luginbuhl, Rob & de Vos, Aart, 1999. "Bayesian Analysis of an Unobserved-Component Time Series Model of GDP with Markov-Switching and Time-Varying Growths," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(4), pages 456-65, October.
  18. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
  19. Masanao Aoki, 1992. "Interactions of Real GNP Business Cycles in a Three Country Time Series Model," UCLA Economics Working Papers 675, UCLA Department of Economics.
  20. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
  21. Boldin Michael D., 1996. "A Check on the Robustness of Hamilton's Markov Switching Model Approach to the Economic Analysis of the Business Cycle," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 1(1), pages 1-14, April.
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Cited by:
  1. Chin Nam Low & Heather Anderson & Ralph D. Snyder, 2006. "Beveridge-Nelson Decomposition with Markov Switching," Monash Econometrics and Business Statistics Working Papers 17/06, Monash University, Department of Econometrics and Business Statistics.

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