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

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  • 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
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    Citations

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    Cited by:

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    2. Richard Kleijn & Herman K. van Dijk, 2001. "A Bayesian Analysis of the PPP Puzzle using an Unobserved Components Model," Tinbergen Institute Discussion Papers 01-105/4, Tinbergen Institute.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. BAUWENS, Luc & BOS, Charles S. & VAN DIJK, Herman K., 1999. "Adaptive polar sampling with an application to a Bayes measure of value-at-risk," LIDAM Discussion Papers CORE 1999057, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. 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.
    9. Tommaso, Proietti & Stefano, Grassi, 2010. "Bayesian stochastic model specification search for seasonal and calendar effects," MPRA Paper 27305, University Library of Munich, Germany.
    10. 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.
    11. 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.
    12. 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.
    13. Svend Hylleberg, 2006. "Seasonal Adjustment," Economics Working Papers 2006-04, Department of Economics and Business Economics, Aarhus University.
    14. 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.
    15. Koop, Gary & Tobias, Justin L., 2006. "Semiparametric Bayesian inference in smooth coefficient models," Journal of Econometrics, Elsevier, vol. 134(1), pages 283-315, September.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    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.
    21. 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.
    22. 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.

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    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

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