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A time series model with periodic stochastic regime switching

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Author Info
Eric Ghysels

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Abstract

A general class of Markov switching regime time series models is presented that allows one to estimate the nontrivial interdependencies between different types of cycles which make the economy grow at an unsteady rate. The paper further explores results obtained in Ghysels (1991b) suggesting that the economy transits from recessions to expansions with an uneven propensity throughout the year. It is also built on the work of Hamilton (1989) who proposed a stochastic switching-regime model for GNP and has important connections with hidden periodic structures discussed by Tiao and Grupe (1980) or Hansen and Sargent (1990), for instance. The time series models we present may have periodic transition probabilities and the drifts may be seasonal. In the latter case, the model exhibits seasonal dummy variation that may change with the stage of the business cycle. While the model is intrinsically nonlinear and stochastic, it produces a linear representation with seasonal effects that appear to be deterministic. The paper provides an elaborate discussion of the regularity conditions for a well-defined covariance structure including explicit formula for characterizing first and second moments. Finally, we present empirical evidence using U.S. GNP data series which tends to support a periodic structure for switching probabilities. The most significant result is the following: it is found that the seasonal in GNP growth significantly affects switching probabilities for regime switches in the nonseasonal growth of GNP. We also analyze the out-of-sample forecast performance of the different models and find that the models exploiting seasonality in transition probabilities perform best.

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Paper provided by Federal Reserve Bank of Minneapolis in its series Discussion Paper / Institute for Empirical Macroeconomics with number 84.

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Date of creation: 1993
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Handle: RePEc:fip:fedmem:84

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Keywords: Time-series analysis;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Engel, Charles & Hamilton, James D, 1990. "Long Swings in the Dollar: Are They in the Data and Do Markets Know It?," American Economic Review, American Economic Association, vol. 80(4), pages 689-713, September. [Downloadable!] (restricted)
  2. Hans Franses, Philip, 1992. "Testing for seasonality," Economics Letters, Elsevier, vol. 38(3), pages 259-262, March. [Downloadable!] (restricted)
  3. Osborn, Denise R., 1991. "The implications of periodically varying coefficients for seasonal time-series processes," Journal of Econometrics, Elsevier, vol. 48(3), pages 373-384, June. [Downloadable!] (restricted)
  4. Phillips, Kerk L., 1991. "A two-country model of stochastic output with changes in regime," Journal of International Economics, Elsevier, vol. 31(1-2), pages 121-142, August. [Downloadable!] (restricted)
  5. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July. [Downloadable!] (restricted)
  6. John Geweke, 1992. "Priors for macroeconomic time series and their application," Discussion Paper / Institute for Empirical Macroeconomics 64, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  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. 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. [Downloadable!] (restricted)
  9. Hylleberg, S. & Engle, R. F. & Granger, C. W. J. & Yoo, B. S., 1990. "Seasonal integration and cointegration," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 215-238. [Downloadable!] (restricted)
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  10. Ghysels, E., 1991. "On Scoring Asymmetric Periodic Probability Models of Turning-Point Forecasts," Cahiers de recherche 9130, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
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  11. Hamilton, James D, 1991. "A Quasi-Bayesian Approach to Estimating Parameters for Mixtures of Normal Distributions," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(1), pages 27-39, January.
  12. Ghysels, E. & Lee, H.S. & Siklos, P.L., 1992. "On the (Mis)Specification of Seasonality and Its Consequences: an Empirical Investigation with U.S. Data," Cahiers de recherche 9237, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  13. Lars Peter Hansen & Thomas J. Sargent, 1990. "Recursive Linear Models of Dynamic Economies," NBER Working Papers 3479, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  14. Ghysels, Eric, 1994. "On the Periodic Structure of the Business Cycle," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 289-98, July.
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  15. Newey, Whitney K & West, Kenneth D, 1987. "Hypothesis Testing with Efficient Method of Moments Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(3), pages 777-87, October. [Downloadable!] (restricted)
  16. Osborn, Denise R & Smith, Jeremy P, 1989. "The Performance of Periodic Autoregressive Models in Forecasting Seasonal U. K. Consumption," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(1), pages 117-27, January.
  17. Todd, Richard M., 1990. "Periodic linear-quadratic methods for modeling seasonality," Journal of Economic Dynamics and Control, Elsevier, vol. 14(3-4), pages 763-795, October. [Downloadable!] (restricted)
  18. Ghysels, E., 1990. "On the Economic and Econometrics of Seasonality," Cahiers de recherche 9028, Universite de Montreal, Departement de sciences economiques.
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  19. Ghysels, Eric & Perron, Pierre, 1993. "The effect of seasonal adjustment filters on tests for a unit root," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 57-98. [Downloadable!] (restricted)
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  20. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70. [Downloadable!] (restricted)
  21. Osborn, Denise R, 1988. "Seasonality and Habit Persistence in a Life Cycle Model of Consumptio n," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 3(4), pages 255-66, October-D. [Downloadable!] (restricted)
  22. Bell, William R & Hillmer, Steven C, 1984. "Issues Involved with the Seasonal Adjustment of Economic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 291-320, October.
  23. Hansen, Lars Peter & Sargent, Thomas J., 1993. "Seasonality and approximation errors in rational expectations models," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 21-55. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Tim Bollerslev & Eric Ghysels, 1994. "On Periodic Autogressive Conditional Heteroskedasticity," CIRANO Working Papers 94s-03, CIRANO. [Downloadable!]
  2. Eric Ghysels & Robert E. McCulloch & Ruey S. Tsay, 1994. "Bayesian Inference for Periodic Regime-Switching Models," CIRANO Working Papers 94s-15, CIRANO. [Downloadable!]
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  3. Geert Bekaert & Campbell R. Harvey, 1994. "Time-Varying World Market Integration," NBER Working Papers 4843, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  4. Marcelle Chauvet, 2000. "Leading Indicators of Inflation for Brazil," Working Papers Series 7, Central Bank of Brazil, Research Department. [Downloadable!]
  5. Margaret M. McConnell & Gabriel Perez Quiros, 1997. "Output fluctuations in the United States: what has changed since the early 1980s?," Research Paper 9735, Federal Reserve Bank of New York. [Downloadable!]
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