Hostname: page-component-5c6d5d7d68-sv6ng Total loading time: 0 Render date: 2024-08-09T13:43:54.200Z Has data issue: false hasContentIssue false
  • English
  • Français

THE ASYMPTOTIC DISTRIBUTION OF THE COINTEGRATION RANK ESTIMATOR UNDER THE AKAIKE INFORMATION CRITERION

Published online by Cambridge University Press:  01 August 2004

George Kapetanios
George Kapetanios
Affiliation:
Queen Mary University of London
Get access Rights & Permissions [Opens in a new window]

Abstract

We derive the asymptotic distribution of the estimate of the cointegration rank of a multivariate model when Akaike's information criterion is used. It is shown that the use of this criterion is ill-advised given that the estimate is severely upward biased even asymptotically.I thank the editor, Professor Peter Phillips, and three anonymous referees for comments and suggestions that improved this paper significantly. All remaining errors are my own.

Type
MISCELLANEA
Information
Econometric Theory , Volume 20 , Issue 4 , August 2004 , pp. 735 - 742
Copyright
© 2004 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Akaike, H. (1973) Information theory and an extension of the maximum likelihood principle. In B.N. Petrov and F. Csaki (eds.), 2nd International Symposium on Information Theory, pp. 267–281. Akademiai Kiado.
Aznar, A. & M. Salvador (2000) Selecting the Rank of the Cointegration Space and the Form of the Intercept Using an Information Criterion. Econometric Theory 18, 926–947.Google Scholar
Bierens, H. (1997) Nonparametric cointegration analysis. Journal of Econometrics 77, 379–404.Google Scholar
Chao, J. & P.C.B. Phillips (1999) Model selection in partially nonstationary vector autoregressive processes with reduced rank structure. Journal of Econometrics 91, 227–272.Google Scholar
Christoffersen, P.F. & F.X. Diebold (1998) Cointegration and long horizon forecasting. Journal of Business and Economic Statistics 16, 450–458.Google Scholar
Hannan, E.J. & B.G. Quinn (1979) The determination of the order of an autoregression. Journal of the Royal Statistical Society, Series B 41, 190–195.Google Scholar
Johansen, S. (1988) Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control 12, 231–254.Google Scholar
Kapetanios, G. (2001) Model selection in threshold models. Journal of Time Series Analysis 22, 733–754.Google Scholar
Konishi, S. & G. Kitagawa (1996) Generalised information criteria in model selection. Biometrika 83, 875–890.Google Scholar
Lütkepohl, H. (1991) Introduction to Multiple Time Series Analysis. Springer.
Paulsen, J. (1984) Order determination of multivariate autoregressive time series with unit roots. Journal of Time Series Analysis 5, 115–127.Google Scholar
Pesaran, M.H. & B. Pesaran (1997) Microfit 4.0. Oxford University Press.
Phillips, P.C.B. (1996) Econometric model determination. Econometrica 64, 763–812.Google Scholar
Phillips, P.C.B. & S. Ouliaris (1988) Testing for cointegration using principal components methods. Journal of Economic Dynamics and Control 12, 205–230.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. & W. Ploberger (1996) An asymptotic theory of Bayesian inference for time series. Econometrica 63, 381–412.Google Scholar
Schwarz, G. (1978) Estimating the dimension of a model. Annals of Statistics 6, 461–464.Google Scholar
Shibata, R. (1976) Selection of the order of an autoregressive model by Akaike's information criterion. Biometrika 63, 117–126.Google Scholar
Shibata, R. (1980) Asymptotically efficient selection of the order of the model for estimating parameters of a linear process. Annals of Statistics 8, 147–164.Google Scholar
Sin, C.Y. & H. White (1996) Information criteria for selecting possibly misspecified parametric models. Journal of Econometrics 71, 207–225.Google Scholar
Snell, A. (1999) Testing for r versus r − 1 cointegrating vectors. Journal of Econometrics 88, 151–191.Google Scholar
Stock, J. & M. Watson (1988) Testing for common trends. Journal of American Statistical Association 83, 1097–1107.Google Scholar