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A Time Series Model with Periodic Stochastic Regime Switching

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  • Ghysels, E.

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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Suggested Citation

  • Ghysels, E., 1993. "A Time Series Model with Periodic Stochastic Regime Switching," Cahiers de recherche 9314, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  • Handle: RePEc:mtl:montec:9314
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    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Ghysels, Eric & Lee, Hahn S & Siklos, Pierre L, 1993. "On the (Mis)Specification of Seasonality and Its Consequences: An Empirical Investigation with U.S. Data," Empirical Economics, Springer, vol. 18(4), pages 747-760.
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    5. Ghysels, Eric, 1994. "On the Periodic Structure of the Business Cycle," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 289-298, July.
    6. Garcia, Rene & Perron, Pierre, 1996. "An Analysis of the Real Interest Rate under Regime Shifts," The Review of Economics and Statistics, MIT Press, vol. 78(1), pages 111-125, February.
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    20. Ghysels, E., 1991. "On Scoring Asymmetric Periodic Probability Models of Turning-Point Forecasts," Cahiers de recherche 9130, Universite de Montreal, Departement de sciences economiques.
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    Cited by:

    1. Eric Ghysels & Robert E. McCulloch & Ruey S. Tsay, 1998. "Bayesian inference for periodic regime-switching models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(2), pages 129-143.
    2. Tim Bollerslev & Eric Ghysels, 1994. "On Periodic Autogressive Conditional Heteroskedasticity," CIRANO Working Papers 94s-03, CIRANO.
    3. Margaret M. McConnell & Gabriel Perez-Quiros, 2000. "Output fluctuations in the United States: what has changed since the early 1980s?," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
    4. Ghysels, Eric, 1997. "On seasonality and business cycle durations: A nonparametric investigation," Journal of Econometrics, Elsevier, vol. 79(2), pages 269-290, August.
    5. Bekaert, Geert & Harvey, Campbell R, 1995. "Time-Varying World Market Integration," Journal of Finance, American Finance Association, vol. 50(2), pages 403-444, June.
    6. Amato, Amedeo & Tronzano, Marco, 2000. "Fiscal policy, debt management and exchange rate credibility: Lessons from the recent Italian experience," Journal of Banking & Finance, Elsevier, vol. 24(6), pages 921-943, June.

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