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Testing for Integration using Evolving Trend and Seasonals Models: A Bayesian Approach

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  • Gary Koop

    (University of Edinburgh)

  • Herman K. van Dijk

    () (Erasmus University Rotterdam)

Abstract

In this paper, we make use of state space models toinvestigate the presence of stochastic trends in economic time series. Amodel is specified where such a trend can enter either in the autoregressiverepresentation or in a separate state equation. Tests based on the formerare analogous to Dickey-Fuller tests of unit roots, while the latter areanalogous to KPSS tests of trend-stationarity. We use Bayesian methods tosurvey the properties of the likelihood function in such models and tocalculate posterior odds ratios comparing models with and without stochastictrends. We extend these ideas to the problem of testing for integration atseasonal frequencies and show how our techniques can be used to carry outBayesian variants of either the HEGY or Canova-Hansen test. Stochasticintegration rules, based on Markov Chain Monte Carlo, as well asdeterministic integration rules are used. Strengths and weaknesses of eachapproach are indicated.

Suggested Citation

  • Gary Koop & Herman K. van Dijk, 1999. "Testing for Integration using Evolving Trend and Seasonals Models: A Bayesian Approach," Tinbergen Institute Discussion Papers 99-072/4, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:19990072
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    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. 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.
    4. Franses, Philip Hans, 1996. "Periodicity and Stochastic Trends in Economic Time Series," OUP Catalogue, Oxford University Press, number 9780198774549.
    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. 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.
    7. 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.
    8. Shephard, Neil, 1993. "Distribution of the ML Estimator of an MA(1) and a local level model," Econometric Theory, Cambridge University Press, vol. 9(03), pages 377-401, June.
    9. 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.
    10. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
    11. Dale J. Poirier, 1995. "Intermediate Statistics and Econometrics: A Comparative Approach," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262161494, January.
    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. 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, August.
    14. 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..
    15. 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..
    16. 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.
    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. 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.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. Koop, Gary, 1992. "'Objective' Bayesian Unit Root Tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(1), pages 65-82, Jan.-Marc.
    24. 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.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    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. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Svend Hylleberg, 2006. "Seasonal Adjustment," Economics Working Papers 2006-04, Department of Economics and Business Economics, Aarhus University.
    10. 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.
    11. Koop, Gary & Tobias, Justin L., 2006. "Semiparametric Bayesian inference in smooth coefficient models," Journal of Econometrics, Elsevier, vol. 134(1), pages 283-315, September.
    12. 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.
    13. 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.
    14. 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.
    15. Tommaso, Proietti & Stefano, Grassi, 2010. "Bayesian stochastic model specification search for seasonal and calendar effects," MPRA Paper 27305, University Library of Munich, Germany.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.

    More about this item

    Keywords

    State space models; Bayes Factor; Gibbs sampler; unit root; seasonality;

    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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