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

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Author Info

  • Gary Koop

    (University of Edinburgh)

  • Herman K. van Dijk

    ()
    (Erasmus University Rotterdam)

  • Henk Hoek

    (Erasmus University Rotterdam)

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-Fullertests 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. In addition, we extend these ideas to the problem of testing for integration at seasonal frequencies and show how techniques can be used to carry out Bayesian variants of HEGY test or the Canova-Hansen test.

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File URL: http://papers.tinbergen.nl/97078.pdf
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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 97-078/4.

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Date of creation: 08 Aug 1997
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Handle: RePEc:dgr:uvatin:19970078

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Web page: http://www.tinbergen.nl

Related research

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

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References

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  1. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  2. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1996. "Stochastic Volatility: Likelihood Inference And Comparison With Arch Models," Econometrics 9610002, EconWPA.
  3. Hylleberg, S. & Pagan, A.R., 1995. "Seasonal Integration and the Evolving Seasonals Model," Papers 281, Australian National University - Department of Economics.
  4. GHYSELS, Eric & HARVEY, Andrew & RENAULT, Eric, 1995. "Stochastic Volatility," CORE Discussion Papers 1995069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. 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.
  6. Kwiatkowski, D. & Phillips, P.C.B. & Schmidt, P., 1990. "Testing the Null Hypothesis of Stationarity Against the Alternative of Unit Root : How Sure are we that Economic Time Series have a Unit Root?," Papers 8905, Michigan State - Econometrics and Economic Theory.
  7. 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.
  8. Stock, James H & Watson, Mark W, 1988. "Variable Trends in Economic Time Series," Journal of Economic Perspectives, American Economic Association, vol. 2(3), pages 147-74, Summer.
  9. Peter C. Schotman & Herman K. van Dijk, 1991. "On Bayesian routes to unit roots," Discussion Paper / Institute for Empirical Macroeconomics 43, Federal Reserve Bank of Minneapolis.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. Min, C.K. & Zellner, A., 1992. ""Bayesian and Non-Bayesian Methods for Combining Models and Forecasts with Applications to Forecasting International Growth Rates"," Papers 90-92-23, California Irvine - School of Social Sciences.
  16. 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.
  17. Bos, C.S. & Mahieu, R.J. & van Dijk, H.K., 1999. "Daily exchange rate behaviour and hedging of currency risk," Econometric Institute Research Papers EI 9936/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  18. 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 333-64, Oct.-Dec..
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  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. repec:fth:erroem:9936/a is not listed on IDEAS
  22. Gary Koop & Simon M. Potter, 1999. "Are apparent findings of nonlinearity due to structural instability in economic time series?," Staff Reports 59, Federal Reserve Bank of New York.
  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. Franses, Philip Hans, 1996. "Periodicity and Stochastic Trends in Economic Time Series," OUP Catalogue, Oxford University Press, number 9780198774549, September.
  26. 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 237-52, July.
  27. 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.
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