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A ROBUST BAYESIAN APPROACH FOR UNIT ROOT TESTING

Published online by Cambridge University Press:  05 April 2007

Caterina Conigliani  and
Fulvio Spezzaferri
Caterina Conigliani
Affiliation:
Università Roma Tre
Fulvio Spezzaferri
Affiliation:
Università di Roma “La Sapienza”
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Abstract

In this paper we deal with the identification of an autoregressive model for an observed time series and the detection of a unit root in its characteristic polynomial. This is a big issue concerned with distinguishing stationary time series from time series for which differencing is required to induce stationarity. We consider a Bayesian approach, and particular attention is devoted to the problem of the sensitivity of the standard Bayesian analysis with respect to the choice of the prior distribution for the autoregressive coefficients.We thank three anonymous referees for their useful comments, which have improved the final version of the paper.

Information

Type
Research Article
Information
Econometric Theory , Volume 23 , Issue 3 , June 2007 , pp. 440 - 463
Copyright
© 2007 Cambridge University Press

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References

REFERENCES

Barbieri, M. & C. Conigliani (1998) Bayesian analysis of autoregressive time series with change points. Journal of the Italian Statistical Society 7, 243–255.Google Scholar
Barbieri, M. & C. Conigliani (2000) Fractional Bayes factors for the analysis of autoregressive models with possible unit roots. In Proceedings of the XL Riunione Scientifica della Società Italiana di Statistica, pp. 137–140. ISTAT Centro Stampa Roma.
Berger, J.O. & L.R. Pericchi (1996) The intrinsic Bayes factor for model selection and prediction. Journal of the American Statistical Association 91, 109–122.Google Scholar
Berger, J.O. & R.-Y. Yang (1994) Noninformative priors and Bayesian testing for the AR(1) model. Econometric Theory 10, 461–482.Google Scholar
Box, G.E.P., G.M. Jenkins, & G. Reinsel (1994) Time Series Analysis, Forecasting and Control, 3rd ed. Prentice-Hall.
Conigliani, C. & A. O'Hagan (2000) Sensitivity of the fractional Bayes factor to prior distributions. Canadian Journal of Statistics 28, 343–352.Google Scholar
De Santis, F. & F. Spezzaferri (1997) Alternative Bayes factors for model selection. Canadian Journal of Statistics 25, 503–515.Google Scholar
De Santis, F. & F. Spezzaferri (1999) Methods for default and robust Bayesian model comparison: The fractional Bayes factor approach. International Statistical Review 67, 267–286.Google Scholar
De Santis, F. & F. Spezzaferri (2001) Consistent fractional Bayes factor for nested normal linear models. Journal of Statistical Planning and Inference 97, 305–321.Google Scholar
Galbraith, R.F. & J.I. Galbraith (1974) On the inverses of some patterned matrices arising in the theory of stationary time series. Journal of Applied Probability 11, 63–71.Google Scholar
Lubrano, M. (1995) Testing for unit roots in a Bayesian framework. Journal of Econometrics 69, 81–109.Google Scholar
Marinucci, D. & L. Petrella (1999) Noninformative Bayesian analysis for stationary and nonstationary AR(1) time series. In J.M. Bernardo, J.O. Berger, A.P. Dawid, & A.F.M. Smith (eds.), Bayesian Statistics 6, pp. 821–828. Oxford University Press.
Marriott, J. & P. Newbold (1998) Bayesian comparison of ARIMA and stationary ARMA models. International Statistical Review 66, 323–336.Google Scholar
Monahan, J.F. (1984) A note on enforcing stationarity in autoregressive-moving average models. Biometrika 71, 403–404.Google Scholar
O'Hagan, A. (1991) Discussion of Posterior Bayes Factors by M. Aitkin. Journal of the Royal Statistical Society, Series B 53, 136.Google Scholar
O'Hagan, A. (1995) Fractional Bayes factor for model comparison (with discussion). Journal of the Royal Statistical Society, Series B 57, 99–138.Google Scholar
O'Hagan, A. (1997) Properties of intrinsic and fractional Bayes factors. Test 6, 101–118.Google Scholar
Pantula, S.G., G. Gonzales-Farias, & W.A. Fuller (1994) A comparison of unit-root test criteria. Journal of Business & Economic Statistics 12, 449–459.Google Scholar
Phillips, P.C.B. (1991a) To criticize the critics: An objective Bayesian analysis of stochastic trends. Journal of Applied Econometrics 6, 333–364.Google Scholar
Phillips, P.C.B. (1991b) Bayesian routes and unit roots: De rebus prioribus semper est disputandum. Journal of Applied Econometrics 6, 435–474.Google Scholar
Phillips, P.C.B. & W. Ploberger (1994) Posterior odds testing for a unit root with data-based model selection. Econometric Theory 10, 774–808.Google Scholar
Phillips, P.C.B. & Z. Xiao (1998) A primer on unit root testing. Journal of Economic Surveys 12, 423–469.Google Scholar
Schotman, P.C. & H.K. Van Dijk (1991a) A Bayesian analysis of the unit root hypothesis in real exchange rate. Journal of Econometrics 49, 195–238.Google Scholar
Schotman, P.C. & H.K. Van Dijk (1991b) On Bayesian routes to unit roots. Journal of Applied Econometrics 6, 387–401.Google Scholar
Sims, C. (1988) Bayesian skepticism on unit root econometrics. Journal of Economic Dynamics and Control 12, 463–474.Google Scholar
Sims, C. & H. Uhlig (1991) Understanding unit rooters: A helicopter tour. Econometrica 59, 1591–1599.Google Scholar
Uhlig, H. (1994a) On Jeffreys prior when using the exact likelihood function. Econometric Theory 10, 633–644.Google Scholar
Uhlig, H. (1994b) What macroeconomists should know about unit roots. Econometric Theory 10, 645–671.Google Scholar
Varshavsky, J.A. (1996) Intrinsic Bayes factors for model selection with autoregressive data. In J.M. Bernardo, J.O. Berger, A.P. Dawid, & A.F.M. Smith (eds.), Bayesian Statistics 5, pp. 757–763. Oxford University Press.
Zivot, E. (1994) A Bayesian analysis of the unit root hypothesis within an unobserved components model. Econometric Theory 10, 552–578.Google Scholar