Hostname: page-component-745bb68f8f-5r2nc Total loading time: 0 Render date: 2025-01-11T23:18:16.405Z Has data issue: false hasContentIssue false
  • English
  • Français

A RESIDUAL-BASED TEST FOR STOCHASTIC COINTEGRATION

Published online by Cambridge University Press:  15 March 2006

Brendan McCabe ,
Stephen Leybourne  and
David Harris
Brendan McCabe
Affiliation:
University of Liverpool
Stephen Leybourne
Affiliation:
University of Nottingham
David Harris
Affiliation:
University of Melbourne
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider the problem of hypothesis testing in a modified version of the stochastic integration and cointegration framework of Harris, McCabe, and Leybourne (2002, Journal of Econometrics 111, 363–384). This nonlinear setup allows for volatility in excess of that catered for by the standard integration/cointegration paradigm through the introduction of nonstationary heteroskedasticity. We propose a test for stochastic cointegration against the alternative of no cointegration and a secondary test for stationary cointegration against the heteroskedastic alternative. Asymptotic distributions of these tests under their respective null hypotheses are derived, and consistency under their respective alternatives is established. Monte Carlo evidence suggests that the tests will perform well in practice. An empirical application to the term structure of interest rates is also given.We are most grateful to the Associate Editor and two anonymous referees for providing helpful comments on earlier versions of this paper.

Type
Research Article
Information
Econometric Theory , Volume 22 , Issue 3 , June 2006 , pp. 429 - 456
Copyright
© 2006 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

Bernard, A.B. & S.N. Durlauf (1996) Interpreting tests of the convergence hypothesis. Journal of Econometrics 71, 161–173.CrossRefGoogle Scholar
Beveridge, S. & C. R. Nelson (1981) A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the business cycle. Journal of Monetary Economics 7, 151–174.CrossRefGoogle Scholar
Busetti, F. & A.M.R. Taylor (2003) Variance shifts, structural breaks and stationarity tests. Journal of Business & Economic Statistics 21, 510–531.CrossRefGoogle Scholar
Campbell, J.Y. & R.J. Shiller (1987) Cointegration and tests of present value models. Journal of Political Economy 95, 1062–1088.CrossRefGoogle Scholar
Engle, R.F. & C.W.J. Granger (1987) Cointegration and error correction: Representation, estimation and testing. Econometrica 55, 251–276.CrossRefGoogle Scholar
Granger, C.W.J. & N.R. Swanson (1997) An introduction to stochastic unit root processes. Journal of Econometrics 80, 35–62.CrossRefGoogle Scholar
Hansen, B.E. (1992a) Heteroscedastic cointegration. Journal of Econometrics 54, 139–158.Google Scholar
Hansen, B.E. (1992b) Convergence to stochastic integrals for dependent heterogeneous processes. Econometric Theory 8, 489–500.Google Scholar
Harris, D., B.P.M. McCabe, & S.J. Leybourne (2002) Stochastic cointegration: Estimation and inference. Journal of Econometrics 111, 363–384.CrossRefGoogle Scholar
Harris, D., B.P.M. McCabe, & S.J. Leybourne (2003) Some limit theory for infinite order autocovariances. Econometric Theory 19, 829–864.Google Scholar
Hobijn, B., P.H. Franses, & M. Ooms (1998) Generalizations of the KPSS-Test for Stationarity. Econometric Institute Working paper, Erasmus University, Rotterdam.
Kwiatkowski, D., P.C.B. Phillips, P. Schmidt, & Y. Shin (1992) Testing the null of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root? Journal of Econometrics 54, 159–178.Google Scholar
Leybourne, S.J., B.P.M. McCabe, & A.R. Tremayne (1996) Can economic time series be differenced to stationarity? Journal of Business & Economic Statistics 14, 435–446.Google Scholar
McCabe, B.P.M. & S.J. Leybourne (2000) A general method of testing for random parameter variation in statistical models. In R.D.H Heijmans, D.S.G. Pollock, & A. Satorra (eds.), Innovations in Multivariate Statistical Analysis: A Festschrift for Heinz Neudecker, pp. 75–85. Kluwer.
Newey, W.K. & K.D. West (1994) Automatic lag selection in covariance estimation. Review of Economic Studies 61, 631–654.CrossRefGoogle Scholar
Phillips, P.C.B. & V. Solo (1992) Asymptotics for linear processes. Annals of Statistics 20, 971–1001.CrossRefGoogle Scholar
Psaradakis, Z., M. Sola, & F. Spagnolo (2001) A simple procedure for detecting periodically collapsing rational bubbles. Economics Letters 72, 317–323.CrossRefGoogle Scholar
Saikkonen, P. (1991) Asymptotically efficient estimation of cointegration regressions. Econometric Theory 7, 1–21.Google Scholar
Shin, Y. (1994) A residual based test of the null of cointegration against the alternative of no cointegration. Econometric Theory 10, 91–115.CrossRefGoogle Scholar
Wu, J.-L. & S.-L. Chen (1997) Can nominal exchange rates be differenced to stationarity? Economics Letters 55, 397–402.Google Scholar