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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.

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Bibliographic Info

Paper provided by Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute in its series Econometric Institute Research Papers with number EI 9934/A.

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Date of creation: 13 Oct 1999
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Handle: RePEc:ems:eureir:1603

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Keywords: Bayes factor; Gibbs sampler; seasonality; state space models; unit root;

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References

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  1. Schotman, Peter C & van Dijk, Herman K, 1991. "On Bayesian Routes to Unit Roots," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 6(4), pages 387-401, Oct.-Dec..
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  5. Hylleberg, S. & Engle, R.F. & Granger, C.W.J. & Yoo, B.S., 1988. "Seasonal, Integration And Cointegration," Papers, Pennsylvania State - Department of Economics 6-88-2, Pennsylvania State - Department of Economics.
  6. Kim, Sangjoon & Shephard, Neil & Chib, Siddhartha, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 65(3), pages 361-93, July.
  7. Hylleberg, S. & Pagan, A.R., 1995. "Seasonal Integration and the Evolving Seasonals Model," Papers, Australian National University - Department of Economics 281, Australian National University - Department of Economics.
  8. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 9613, Universite de Montreal, Departement de sciences economiques.
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  15. repec:fth:erroem:9936/a is not listed on IDEAS
  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, American Economic Association, vol. 81(3), pages 600-617, June.
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