[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
IDEAS home Printed from https://ideas.repec.org/p/ems/eureir/1603.html
   My bibliography  Save this paper

Testing for integration using evolving trend and seasonal models: A Bayesian approach

Author

Listed:
  • Koop, G.
  • van Dijk, H.K.
Abstract
In this paper, we make use of state space models to investigate the presence of stochastic trends in economic time series. A model is specified where such a trend can enter either in the autoregressive representation or in a separate state equation. Tests based on the former are analogous to Dickey-Fuller tests of unit roots, while the latter are analogous to KPSS tests of trend-stationarity. We use Bayesian methods to survey the properties of the likelihood function in such models and to calculate posterior odds ratios comparing models with and without stochastic trends. We extend these ideas to the problem of testing for integration at seasonal frequencies and show how our techniques can be used to carry out Bayesian variants of either the HEGY or Canova-Hansen test. Stochastic integration rules, based on Markov Chain Monte Carlo, as well as deterministic integration rules are used. Strengths and weaknesses of each approach are indicated.

Suggested Citation

  • Koop, G. & van Dijk, H.K., 1999. "Testing for integration using evolving trend and seasonal models: A Bayesian approach," Econometric Institute Research Papers EI 9934/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:1603
    as

    Download full text from publisher

    File URL: https://repub.eur.nl/pub/1603/feweco19991013115224.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Koop, Gary & Potter, Simon M, 1999. "Dynamic Asymmetries in U.S. Unemployment," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(3), pages 298-312, July.
    2. Chib, Siddhartha & Greenberg, Edward, 1994. "Bayes inference in regression models with ARMA (p, q) errors," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 183-206.
    3. Phillips, P C B, 1991. "To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 333-364, Oct.-Dec..
    4. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    5. 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.
    6. Stock, James H & Watson, Mark W, 1988. "Variable Trends in Economic Time Series," Journal of Economic Perspectives, American Economic Association, vol. 2(3), pages 147-174, Summer.
    7. Franses, Philip Hans, 1996. "Periodicity and Stochastic Trends in Economic Time Series," OUP Catalogue, Oxford University Press, number 9780198774549.
    8. Charles S. Bos & Ronald J. Mahieu & Herman K. Van Dijk, 2000. "Daily exchange rate behaviour and hedging of currency risk," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(6), pages 671-696.
    9. Min, Chung-ki & Zellner, Arnold, 1993. "Bayesian and non-Bayesian methods for combining models and forecasts with applications to forecasting international growth rates," Journal of Econometrics, Elsevier, vol. 56(1-2), pages 89-118, March.
    10. Hylleberg, S. & Pagan, A. R., 1997. "Seasonal integration and the evolving seasonals model," International Journal of Forecasting, Elsevier, vol. 13(3), pages 329-340, September.
    11. 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.
    12. Schotman, Peter & van Dijk, Herman K., 1991. "A Bayesian analysis of the unit root in real exchange rates," Journal of Econometrics, Elsevier, vol. 49(1-2), pages 195-238.
    13. John Geweke, 1999. "Using Simulation Methods for Bayesian Econometric Models," Computing in Economics and Finance 1999 832, Society for Computational Economics.
    14. Canova, Fabio & Hansen, Bruce E, 1995. "Are Seasonal Patterns Constant over Time? A Test for Seasonal Stability," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 237-252, July.
    15. Leybourne, S J & McCabe, B P M, 1994. "A Consistent Test for a Unit Root," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 157-166, April.
    16. DeJong, David N & Whiteman, Charles H, 1991. "The Temporal Stability of Dividends and Stock Prices: Evidence from the Likelihood Function," American Economic Review, American Economic Association, vol. 81(3), pages 600-617, June.
    17. John Geweke, 1999. "Using simulation methods for bayesian econometric models: inference, development,and communication," Econometric Reviews, Taylor & Francis Journals, vol. 18(1), pages 1-73.
    18. Shephard, Neil, 1993. "Distribution of the ML Estimator of an MA(1) and a local level model," Econometric Theory, Cambridge University Press, vol. 9(3), pages 377-401, June.
    19. Schotman, Peter C., 1994. "Priors For The Ar(1) Model: Parameterization Issues and Time Series Considerations," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 579-595, August.
    20. Kato, Hiroko & Naniwa, Sadao & Ishiguro, Makio, 1996. "A bayesian multivariate nonstationary time series model for estimating mutual relationships among variables," Journal of Econometrics, Elsevier, vol. 75(1), pages 147-161, November.
    21. Dale J. Poirier, 1995. "Intermediate Statistics and Econometrics: A Comparative Approach," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262161494, April.
    22. Schotman, Peter C & van Dijk, Herman K, 1991. "On Bayesian Routes to Unit Roots," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 387-401, Oct.-Dec..
    23. Shively, Thomas S. & Kohn, Robert, 1997. "A Bayesian approach to model selection in stochastic coefficient regression models and structural time series models," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 39-52.
    24. Koop, Gary, 1992. "'Objective' Bayesian Unit Root Tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(1), pages 65-82, Jan.-Marc.
    25. 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.
    26. Hannan, E J & Terrell, R D & Tuckwell, N E, 1970. "The Seasonal Adjustment of Economic Time Series," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 11(1), pages 24-52, February.
    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. Richard Kleijn & Herman K. van Dijk, 2006. "Bayes model averaging of cyclical decompositions in economic time series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(2), pages 191-212.
    2. Michiel D. de Pooter & René Segers & Herman K. van Dijk, 2006. "On the Practice of Bayesian Inference in Basic Economic Time Series Models using Gibbs Sampling," Tinbergen Institute Discussion Papers 06-076/4, Tinbergen Institute.
    3. Svend Hylleberg, 2006. "Seasonal Adjustment," Economics Working Papers 2006-04, Department of Economics and Business Economics, Aarhus University.
    4. Tommaso Proietti & Stefano Grassi, 2015. "Stochastic trends and seasonality in economic time series: new evidence from Bayesian stochastic model specification search," Empirical Economics, Springer, vol. 48(3), pages 983-1011, May.
    5. Bauwens, Luc & Bos, Charles S. & van Dijk, Herman K. & van Oest, Rutger D., 2004. "Adaptive radial-based direction sampling: some flexible and robust Monte Carlo integration methods," Journal of Econometrics, Elsevier, vol. 123(2), pages 201-225, December.
    6. Kleijn, R.H. & van Dijk, H.K., 2001. "A Bayesian analysis of the PPP puzzle using an unobserved components model," Econometric Institute Research Papers EI 2001-35, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    7. Grassi, S. & Proietti, T., 2014. "Characterising economic trends by Bayesian stochastic model specification search," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 359-374.
    8. Jacek Kwiatkowski, 2008. "Bayesian Analysis of Polish Inflation Rates Using RCA and GLL Models," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 8, pages 129-138.
    9. Philippe J. Deschamps, 2003. "Time-varying intercepts and equilibrium analysis: an extension of the dynamic almost ideal demand model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(2), pages 209-236.
    10. Bauwens, L. & Bos, C.S. & van Dijk, H.K., 1999. "Adaptive Polar Sampling with an Application to a Bayes Measure of Value-at-Risk," Econometric Institute Research Papers TI 99-082/4, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    11. Charles S. Bos & Ronald J. Mahieu & Herman K. Van Dijk, 2000. "Daily exchange rate behaviour and hedging of currency risk," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(6), pages 671-696.
    12. Rodrigo Barbone Gonzalez & Joaquim Lima & Leonardo Marinho, 2015. "Countercyclical Capital Buffers: bayesian estimates and alternatives focusing on credit growth," Working Papers Series 384, Central Bank of Brazil, Research Department.
    13. Harvey, Andrew C. & Trimbur, Thomas M. & Van Dijk, Herman K., 2007. "Trends and cycles in economic time series: A Bayesian approach," Journal of Econometrics, Elsevier, vol. 140(2), pages 618-649, October.
    14. Thomas M. Trimbur, 2006. "Detrending economic time series: a Bayesian generalization of the Hodrick-Prescott filter," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(4), pages 247-273.
    15. D.S. Prasada Rao & Alicia Rambaldi & Howard Doran, 2008. "A Method to Construct World Tables of Purchasing Power Parities and Real Incomes Based on Multiple Benchmarks and Auxiliary Information: Analytical and Empirical Results," CEPA Working Papers Series WP052008, School of Economics, University of Queensland, Australia.
    16. Alicia N. Rambaldi & D.S. Prasada Rao & K. Renuka Ganegodage, 2009. "Spatial Autocorrelation and Extrapolation of Purchasing Power Parities. Modelling and Sensitivity Analysis," CEPA Working Papers Series WP012009, School of Economics, University of Queensland, Australia.
    17. Koop, Gary & Tobias, Justin L., 2006. "Semiparametric Bayesian inference in smooth coefficient models," Journal of Econometrics, Elsevier, vol. 134(1), pages 283-315, September.
    18. de Pooter, M.D. & Ravazzolo, F. & Segers, R. & van Dijk, H.K., 2008. "Bayesian near-boundary analysis in basic macroeconomic time series models," Econometric Institute Research Papers EI 2008-13, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    19. de Pooter, M.D. & Segers, R. & van Dijk, H.K., 2006. "Gibbs sampling in econometric practice," Econometric Institute Research Papers EI 2006-13, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    20. Tommaso, Proietti & Stefano, Grassi, 2010. "Bayesian stochastic model specification search for seasonal and calendar effects," MPRA Paper 27305, University Library of Munich, Germany.
    21. Rodrigo Barbone Gonzalez & Joaquim Lima & Leonardo Marinho, 2015. "Business and Financial Cycles: an estimation of cycles’ length focusing on Macroprudential Policy," Working Papers Series 385, Central Bank of Brazil, Research Department.
    22. Harvey, A.C. & Trimbur, T.M. & van Dijk, H.K., 2004. "Bayes estimates of the cyclical component in twentieth centruy US gross domestic product," Econometric Institute Research Papers EI 2004-45, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

    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. Tommaso Proietti & Stefano Grassi, 2015. "Stochastic trends and seasonality in economic time series: new evidence from Bayesian stochastic model specification search," Empirical Economics, Springer, vol. 48(3), pages 983-1011, May.
    2. de Pooter, M.D. & Ravazzolo, F. & Segers, R. & van Dijk, H.K., 2008. "Bayesian near-boundary analysis in basic macroeconomic time series models," Econometric Institute Research Papers EI 2008-13, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. Nalan Basturk & Cem Cakmakli & S. Pinar Ceyhan & Herman K. van Dijk, 2014. "On the Rise of Bayesian Econometrics after Cowles Foundation Monographs 10, 14," Tinbergen Institute Discussion Papers 14-085/III, Tinbergen Institute, revised 04 Sep 2014.
    4. Nalan Basturk & Cem Cakmakli & S. Pinar Ceyhan & Herman K. van Dijk, 2013. "Historical Developments in Bayesian Econometrics after Cowles Foundation Monographs 10, 14," Tinbergen Institute Discussion Papers 13-191/III, Tinbergen Institute.
    5. Svend Hylleberg, 2006. "Seasonal Adjustment," Economics Working Papers 2006-04, Department of Economics and Business Economics, Aarhus University.
    6. Grassi, S. & Proietti, T., 2014. "Characterising economic trends by Bayesian stochastic model specification search," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 359-374.
    7. Marriott, John & Newbold, Paul, 2000. "The strength of evidence for unit autoregressive roots and structural breaks: A Bayesian perspective," Journal of Econometrics, Elsevier, vol. 98(1), pages 1-25, September.
    8. Liesenfeld, Roman & Richard, Jean-François, 2008. "Improving MCMC, using efficient importance sampling," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 272-288, December.
    9. Stéphane Adjemian & Florian Pelgrin, 2008. "Un regard bayésien sur les modèles dynamiques de la macroéconomie," Economie & Prévision, La Documentation Française, vol. 0(2), pages 127-152.
    10. Hoek, Henk & Lucas, Andre & van Dijk, Herman K., 1995. "Classical and Bayesian aspects of robust unit root inference," Journal of Econometrics, Elsevier, vol. 69(1), pages 27-59, September.
    11. Gabriel Pons Rotger, 2004. "Seasonal Unit Root Testing Based on the Temporal Aggregation of Seasonal Cycles," Economics Working Papers 2004-1, Department of Economics and Business Economics, Aarhus University.
    12. Charles S. Bos & Ronald J. Mahieu & Herman K. Van Dijk, 2000. "Daily exchange rate behaviour and hedging of currency risk," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(6), pages 671-696.
    13. Kleibergen, F.R. & Hoek, H., 1995. "Bayesian analysis of ARMA models using noninformative priors," Other publications TiSEM 81684a10-935f-49c4-b5ab-0, Tilburg University, School of Economics and Management.
    14. Tommaso, Proietti & Stefano, Grassi, 2010. "Bayesian stochastic model specification search for seasonal and calendar effects," MPRA Paper 27305, University Library of Munich, Germany.
    15. Gael Martin, 2001. "Bayesian Analysis Of A Fractional Cointegration Model," Econometric Reviews, Taylor & Francis Journals, vol. 20(2), pages 217-234.
    16. Loukia Meligkotsidou & Elias Tzavalis & Ioannis D. Vrontos, 2004. "A Bayesian Analysis of Unit Roots and Structural Breaks in the Level and the Error Variance of Autoregressive Models," Working Papers 514, Queen Mary University of London, School of Economics and Finance.
    17. Hylleberg, S. & Pagan, A. R., 1997. "Seasonal integration and the evolving seasonals model," International Journal of Forecasting, Elsevier, vol. 13(3), pages 329-340, September.
    18. Lubrano, Michel, 1995. "Testing for unit roots in a Bayesian framework," Journal of Econometrics, Elsevier, vol. 69(1), pages 81-109, September.
    19. Peter C. B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-470, December.
    20. de Pooter, M.D. & Segers, R. & van Dijk, H.K., 2006. "Gibbs sampling in econometric practice," Econometric Institute Research Papers EI 2006-13, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

    More about this item

    Keywords

    Bayes factor; Gibbs sampler; seasonality; state space models; unit root;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

    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:ems:eureir:1603. 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: RePub (email available below). General contact details of provider: https://edirc.repec.org/data/feeurnl.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.