Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-12-02T19:14:59.388Z Has data issue: false hasContentIssue false
  • English
  • Français

A MONTE CARLO STUDY ON THE SELECTION OF COINTEGRATING RANK USING INFORMATION CRITERIA

Published online by Cambridge University Press:  22 April 2005

Zijun Wang  and
David A. Bessler
Zijun Wang
Affiliation:
Texas A&M University
David A. Bessler
Affiliation:
Texas A&M University
Get access Rights & Permissions [Opens in a new window]

Abstract

We conduct Monte Carlo simulations to evaluate the use of information criteria (Akaike information criterion [AIC] and Schwarz information criterion [SC]) as an alternative to various probability-based tests for determining cointegrating rank in multivariate analysis. First, information criteria are used to determine cointegrating rank given the lag order in a levels vector autoregression. Second, information criteria are used to determine the lag order and cointegrating rank simultaneously. Results show that AIC has an advantage over trace tests for cointegrated or stationary processes in small samples. AIC does not perform well in large samples. The performance of SC is close to that of the trace test. SC shows better large sample results than AIC and the trace test, even if the series are close to nonstationary series or they contain large negative moving average components. We also find evidence that supports the joint estimation of lag order and cointegrating rank by the SC criterion. We conclude that information criteria can complement traditional parametric tests.We are grateful to Peter C.B. Phillips and an anonymous referee for their comments, which significantly improved the paper.

Type
Research Article
Information
Econometric Theory , Volume 21 , Issue 3 , June 2005 , pp. 593 - 620
Copyright
© 2005 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

Ahn, S.K & C.G. Reinsel (1990) Estimation for partially nonstationary multivariate autoregressive models. Journal of the American Statistical Association 85, 813–823.Google Scholar
Akaike, H. (1973) Information theory and an extension of the maximum likelihood principle. In B.N. Petrov & F. Csaki (eds.), Second International Symposium on Information Theory, pp. 267–281. Akademiai Kiado.
Aznar, A. & M. Salvador (2002) Selecting the rank of cointegration space and the form of the intercept using an information criterion. Econometric Theory 18, 926–947.Google Scholar
Banerjee, A., J.J. Dolado, D.F. Hendry, & G.W. Smith (1986) Exploring equilibrium relationships in econometrics through static models: Some Monte Carlo evidence. Oxford Bulletin of Economics and Statistics 48, 253–277.Google Scholar
Blangiewicz, M. & W. Charemza (1990) Cointegration in small samples: Empirical percentiles, drifting moments and customized testing. Oxford Bulletin of Economics and Statistics 52, 303–315.Google Scholar
Boswijk, H.P. & P.H. Frasnes (1992) Dynamic specification and cointegration. Oxford Bulletin of Economics and Statistics 54, 369–381.Google Scholar
Box, G.E.P. & G.C. Tiao (1977) A canonical analysis of multiple time series. Biometrika 64, 355–365.Google Scholar
Chao, J.C. & P.C.B. Phillips (1999) Model selection in partially nonstationary vector autoregressive processes with reduced rank structure. Journal of Econometrics 91, 227–271.Google Scholar
Cheung, Y.W. & K.S. Lai (1993) Finite sample sizes of Johansen's likelihood ratio tests for cointegration. Oxford Bulletin of Economics and Statistics 55, 313–332.Google Scholar
Doan, T.A. (1996) User's Manual: RATS 4.0. Estima.
Engle, R.F. & C.W.J. Granger (1987) Cointegration and error correction: Representation, estimation and testing. Econometrica 5, 251–276.Google Scholar
Gonzalo, J. (1994) Comparison of five alternative methods of estimating long-run equilibrium relationships. Journal of Econometrics 60, 203–233.Google Scholar
Gonzalo, J. & J.Y. Pitarakis (1999) Dimensionality effect in cointegration analysis. In R.F. Engle & H. White (eds.), Cointegration, Causality and Forecasting: Festschrift in Honour of Clive Granger, pp. 212–229. Oxford: Oxford University Press.
Gonzalo, J. & J.Y. Pitarakis (1998) Specification via model selection in vector error correction models. Economics Letters 60, 321–328.Google Scholar
Hansen, B.E. & P.C.B. Phillips (1990) Estimation and inference in models of cointegration: A simulation study. Advances in Econometrics 8, 225–248.Google Scholar
Hansen, H. & K. Juselius (1995) CATS in RATS. Estima.
Haug, A.A. (1996) Tests for cointegration: A Monte Carlo comparison. Journal of Econometrics 71, 89–115.Google Scholar
Johansen, S. (1988) Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control 12, 231–254.Google Scholar
Johansen, S. (1991) Estimation and hypothesis testing of cointegration vector in Gaussian vector autoregressive models. Econometrica 59, 1551–1580.Google Scholar
Johansen, S. (1992) Determination of cointegration rank in the presence of a linear trend. Oxford Bulletin of Economics and Statistics 54, 383–397.Google Scholar
Johansen, S. (1996) Likelihood-Based Inference in Cointegrated Vector Autoregressive Models. Oxford University Press.
Johansen, S. (2000) A Bartlett correction factor for tests on the cointegrating relations. Econometric Theory 16, 740–778.Google Scholar
Johansen, S. (2002) A small sample correction for the test of cointegrating rank in the vector autoregressions. Econometrica 70, 1929–1961.Google Scholar
Kapetanios, G. (2004) The asymptotic distribution of the cointegration rank estimator under the Akaike information criterion. Econometric Theory 20, 735–742.Google Scholar
Kremers, J.J., N.R. Ericsson, & J.J. Dolado (1992) The power of co-integration tests. Oxford Bulletin of Economics and Statistics 54, 325–348.Google Scholar
Maddala, G.S. & I.M. Kim (1998) Unit Roots, Cointegration, and Structural Change. Cambridge University Press.
Phillips, P.C.B. (1996) Econometric model determination. Econometrica 64, 763–812.Google Scholar
Phillips, P.C.B. & J.W. McFarland (1997) Forward exchange market unbiasedness: The case of the Australian dollar since 1984. Journal of International Money and Finance 16, 885–907.Google Scholar
Phillips, P.C.B. & W. Ploberger (1996) An asymptotic theory of Bayesian inference for time series. Econometrica 64, 381–412.Google Scholar
Podivinsky, J.M. (1990) Testing for a unit root in time series regression. Biometrika 75, 335–346.Google Scholar
Quenouille, M.H. (1957) The Analysis of Multiple Time Series. Griffin.
Reinsel, G.C. (1983) Some results on multivariate autoregressive index models. Biometrika 70, 145–156.Google Scholar
Reinsel, G.C. & R.P. Velu (1998) Multivariate Reduced-Rank Regression. Springer.
Schwarz, G. (1978) Estimating the dimension of a model. Annals of Statistics 8, 461–464.Google Scholar
Stock, J.H. & M.W. Watson (1988) Testing for common trends. Journal of the American Statistical Association 83, 1097–1107.Google Scholar
Tiao, G.C. & R.S. Tsay (1983) Multiple time series modeling and extended sample cross-correlations. Journal of Business and Economic Statistics 1, 43–56.Google Scholar
Tiao, G.C. & R.S. Tsay (1989) Model specification in multivariate time series (with discussion). Journal of the Royal Statistical Society, Series B 51, 157–213.Google Scholar
Toda, H.Y. (1994) Finite sample properties of likelihood ratio tests for cointegrating ranks with linear trends are present. Review of Economics and Statistics 76, 66–79.Google Scholar
Toda, H.Y. (1995) Finite sample performances of likelihood ratio tests for cointegrating ranks in vector autoregressions. Econometric Theory 11, 1015–1032.Google Scholar
Velu, R.P., G.C. Reinsel, & D.W. Wichern (1986) Reduced rank models for multiple time series. Biometrika 73, 105–118.Google Scholar
Wang, Z. & D.A. Bessler (2002) The homogeneity restriction and forecasting performance of VAR-type demand systems: An empirical examination of U.S. meat consumption. Journal of Forecasting 21, 193–206.Google Scholar
Wang, Z. & D.A. Bessler (2004) Forecasting performance of multivariate time series models with full and reduced rank: An empirical examination. International Journal of Forecasting 20, 683–695.Google Scholar