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Bayesian Encompassing Tests of a Unit Root Hypothesis

Published online by Cambridge University Press:  11 February 2009

Jean-Pierre Florens ,
Sophie Larribeau  and
Michel Mouchart
Jean-Pierre Florens
Affiliation:
Université des Sciences Sociales de Toulouse
Sophie Larribeau
Affiliation:
Université des Sciences Sociales de Toulouse
Michel Mouchart
Affiliation:
Université Catholique de Louvain
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Abstract

The object of this paper is to report, for a simple testing problem of a unit root hypothesis, some experience regarding the numerical problems involved by using a Bayesian encompassing test, i.e., a Bayesian procedure that treats the null and the alternative hypotheses as different models, the null one and the alternative one, that share a same sample space but with different parameter spaces. Numerical procedures and efficient simulations are discussed briefly, and the numerical results so obtained are used to evaluate the meaning of the prior specification and of the empirical evidence about a unit root inference.

Type
Articles
Information
Econometric Theory , Volume 10 , Issue 3-4 , August 1994 , pp. 747 - 763
Copyright
Copyright © Cambridge University Press 1994

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References

REFERENCES

1Berk, R.H.Limiting behavior of posterior distributions when the model is incorrect. Annals of Mathematical Statistics 37 (1966): 51–58.CrossRefGoogle Scholar
2Devroye, L.Non-Uniform Random Variate Generation. New York: Springer-Verlag, 1982.Google Scholar
3Dickey, D.A. & Fuller, W.A.. Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica 49 (1981): 1057–1072.CrossRefGoogle Scholar
4Florens, J.P. Parameter sufficiency and encompassing. In Essays in Honour of Edmond Malinvaud, pp. 115–136. Cambridge: MIT Press, 1990.Google Scholar
5Florens, J.P., Hendry, D.F. & Richard, J.P.. Encompassing and specificity. Cahier du Gremaq 91c, Universite des Sciences Sociales, Toulouse, 1991 (Submitted to Econometric Theory).Google Scholar
6Florens, J.P. & Mouchart, M.. Model selection: Some remarks from a Bayesian viewpoint. In Florens, J.P., Mouchart, M. & Simar, L. (eds.), Model Choice, pp. 27–44. Brussels: Publications des Facultés Universitaires, Saint Louis, 1985.Google Scholar
7Florens, J.P. & Mouchart, M.. Bayesian specification tests. In Cornet, B. & Tulkens, H. (eds.), Contributions to Operations Research and Economics, pp. 467–490. Cambridge: MIT Press, 1989.Google Scholar
8Florens, J.P. & Mouchart, M.. Bayesian testing and testing Bayesians. In Maddala, G.S., Rao, C.R. & Vinod, H.D. (eds.), Handbook of Statistics, vol. 11, chap. 11. Amsterdam: North Holland, 1993.Google Scholar
9Florens, J.P., Mouchart, M. & Rolin, J.M.. Elements of Bayesian Statistics. New York: Marcel Dekker, 1990.Google Scholar
10Florens, J.P., Mouchart, M. & Scotto, S.. Approximate sufficiency on the parameter space and model selection. In 44th Session of the International Statistical Institute: Contributed Papers, vol. 2, pp. 763–766, 1983.Google Scholar
11Geweke, J.Bayesian inference in econometric models using Monte-Carlo integration. Econometrica 57 (1989): 1317–1339.CrossRefGoogle Scholar
12Kloek, T. & van Dijk, H.K.. Bayesian estimates of equation systems parameters: An application of integration by Monte-Carlo. Econometrica 46 (1978): 1–20.Google Scholar
13Phillips, P.C.B.Time series regression with a unit root. Econometrica 55 (1987): 277–301.CrossRefGoogle Scholar
14Phillips, P.C.B.To criticize the critics: An objective Bayesian analysis of stochastic trends. Journal of Applied Econometrics 6 (1991): 435–474.Google Scholar
15Schotman, P. & van Dijk, H.K.. A Bayesian analysis of the unit root in real exchange rates. Journal of Econometrics 49 (1991): 195–238.Google Scholar
16Schotman, P. & van Dijk, H.K.. On Bayesian routes to unit roots. Journal of Applied Econometrics 6 (1991): 387–402.Google Scholar
17Serfling, R.J.Approximation Theorems of Mathematical Statistics. New York: Wiley, 1980.Google Scholar
18Sims, C.A.Bayesian skepticism on unit root econometrics. Journal of Economic Dynamics and Control 12 (1988): 463–474.CrossRefGoogle Scholar
19Sims, C.A.Comments on “To criticize the critics” by P.C.B. Phillips. Journal of Applied Econometrics 6 (1991): 423–434.CrossRefGoogle Scholar
20Sims, C.A. & Uhlig, H.. Understanding unit rooters: A helicopter tour. Econometrica 59 (1991).CrossRefGoogle Scholar