IDEAS home Printed from https://ideas.repec.org/p/mtl/montec/9314.html
   My bibliography  Save this paper

A Time Series Model with Periodic Stochastic Regime Switching

Author

Listed:
  • 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.
(This abstract was borrowed from another version of this item.)

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
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Geweke, John, 1994. "Priors for Macroeconomic Time Series and Their Application," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 609-632, August.
    4. 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.
    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.
    7. 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.
    8. Francis X. Diebold & Joon-Haeng Lee & Gretchen C. Weinbach, 1993. "Regime switching with time-varying transition probabilities," Working Papers 93-12, Federal Reserve Bank of Philadelphia.
    9. 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 777-787, October.
    10. Ghysels, E., 1990. "On the Economic and Econometrics of Seasonality," Cahiers de recherche 9028, Universite de Montreal, Departement de sciences economiques.
    11. 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.
    12. 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.
    13. Hylleberg, Svend, 1986. "Seasonality in Regression," Elsevier Monographs, Elsevier, edition 1, number 9780123634559 edited by Shell, Karl.
    14. 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.
    15. Hans Franses, Philip, 1992. "Testing for seasonality," Economics Letters, Elsevier, vol. 38(3), pages 259-262, March.
    16. Nerlove, Marc & Grether, David M. & Carvalho, José L., 1979. "Analysis of Economic Time Series," Elsevier Monographs, Elsevier, edition 1, number 9780125157506 edited by Shell, Karl.
    17. 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.
    18. Bell, William R & Hillmer, Steven C, 1984. "Issues Involved with the Seasonal Adjustment of Time Series: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 343-349, October.
    19. 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 357-384, March.
    20. Lars Peter Hansen & Thomas J. Sargent, 1993. "Recursive linear models of dynamic economies," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
    21. 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.
    22. Ghysels, E., 1991. "On Scoring Asymmetric Periodic Probability Models of Turning-Point Forecasts," Cahiers de recherche 9130, Universite de Montreal, Departement de sciences economiques.
    23. Hansen, B.E., 1991. "The Likelihood Test Under Non-Standard Conditions: Testing the Markov Trend Model of GNP," RCER Working Papers 279, University of Rochester - Center for Economic Research (RCER).
    24. 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.
    25. 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 117-127, January.
    26. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
    27. 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.
    28. Hamilton, James D., 1988. "Rational-expectations econometric analysis of changes in regime : An investigation of the term structure of interest rates," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 385-423.
    29. 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.
    30. 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 255-266, October-D.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Madura, Jeff & Ngo, Thanh & Viale, Ariel M., 2011. "Convergent synergies in the global market for corporate control," Journal of Banking & Finance, Elsevier, vol. 35(9), pages 2468-2478, September.
    5. Serhii Lupenko, 2022. "The Mathematical Model of Cyclic Signals in Dynamic Systems as a Cyclically Correlated Random Process," Mathematics, MDPI, vol. 10(18), pages 1-27, September.
    6. Al-Mohamed, Somar & Elkanj, Nasser & Gangopadhyay, Partha, 2018. "Time-Varying Integration of MENA Stock Markets," International Journal of Development and Conflict, Gokhale Institute of Politics and Economics, vol. 8(2), pages 85-114.
    7. Ghysels, Eric, 1997. "On seasonality and business cycle durations: A nonparametric investigation," Journal of Econometrics, Elsevier, vol. 79(2), pages 269-290, August.
    8. Bekaert, Geert & Harvey, Campbell R, 1995. "Time-Varying World Market Integration," Journal of Finance, American Finance Association, vol. 50(2), pages 403-444, June.
    9. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bollerslev, Tim & Ghysels, Eric, 1996. "Periodic Autoregressive Conditional Heteroscedasticity," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 139-151, April.
    2. Diebold, Francis X & Rudebusch, Glenn D, 1996. "Measuring Business Cycles: A Modern Perspective," The Review of Economics and Statistics, MIT Press, vol. 78(1), pages 67-77, February.
    3. 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.
    4. Chung-Ming Kuan, 2013. "Markov switching model (in Russian)," Quantile, Quantile, issue 11, pages 13-40, December.
    5. Psaradakis, Zacharias & Sola, Martin, 1998. "Finite-sample properties of the maximum likelihood estimator in autoregressive models with Markov switching," Journal of Econometrics, Elsevier, vol. 86(2), pages 369-386, June.
    6. Igor Alexandre Clemente de Morais & Marcelo Savino Portugal, 2003. "Business Cycle in the Industrial Production of Brazilian States," Anais do XXXI Encontro Nacional de Economia [Proceedings of the 31st Brazilian Economics Meeting] e75, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    7. Tim Bollerslev & Eric Ghysels, 1994. "On Periodic Autogressive Conditional Heteroskedasticity," CIRANO Working Papers 94s-03, CIRANO.
    8. Braun, R. Anton & Evans, Charles L., 1995. "Seasonality and equilibrium business cycle theories," Journal of Economic Dynamics and Control, Elsevier, vol. 19(3), pages 503-531, April.
    9. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
    10. Liu, Wen-Hsien & Chyi, Yih-Luan, 2006. "A Markov regime-switching model for the semiconductor industry cycles," Economic Modelling, Elsevier, vol. 23(4), pages 569-578, July.
    11. Uctum, Remzi, 2007. "Économétrie des modèles à changement de régimes : un essai de synthèse," L'Actualité Economique, Société Canadienne de Science Economique, vol. 83(4), pages 447-482, décembre.
    12. Tucker McElroy & Anindya Roy, 2022. "A Review of Seasonal Adjustment Diagnostics," International Statistical Review, International Statistical Institute, vol. 90(2), pages 259-284, August.
    13. Fok, D. & Franses, Ph.H.B.F. & Paap, R., 2005. "Performance of Seasonal Adjustment Procedures: Simulation and Empirical Results," Econometric Institute Research Papers EI 2005-30, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    14. Engel, Charles, 1994. "Can the Markov switching model forecast exchange rates?," Journal of International Economics, Elsevier, vol. 36(1-2), pages 151-165, February.
    15. Hamilton, James D., 1996. "Specification testing in Markov-switching time-series models," Journal of Econometrics, Elsevier, vol. 70(1), pages 127-157, January.
    16. Yuan, Chunming, 2011. "The exchange rate and macroeconomic determinants: Time-varying transitional dynamics," The North American Journal of Economics and Finance, Elsevier, vol. 22(2), pages 197-220, August.
    17. Chevallier, Julien, 2011. "Evaluating the carbon-macroeconomy relationship: Evidence from threshold vector error-correction and Markov-switching VAR models," Economic Modelling, Elsevier, vol. 28(6), pages 2634-2656.
    18. Tomás Barrio & Mariam Camarero & Cecilio Tamarit, 2019. "Testing for Periodic Integration with a Changing Mean," Computational Economics, Springer;Society for Computational Economics, vol. 54(1), pages 45-75, June.
    19. Nurgun Topalli & İbrahim Dogan, 2016. "The structure and sustainability of current account deficit: Turkish evidence from regime switching," The Journal of International Trade & Economic Development, Taylor & Francis Journals, vol. 25(4), pages 570-589, June.
    20. Ghysels, Eric, 1997. "On seasonality and business cycle durations: A nonparametric investigation," Journal of Econometrics, Elsevier, vol. 79(2), pages 269-290, August.

    More about this item

    Keywords

    time series;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mtl:montec:9314. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sharon BREWER (email available below). General contact details of provider: https://edirc.repec.org/data/cdmtlca.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.