Hostname: page-component-89b8bd64d-rbxfs Total loading time: 0 Render date: 2026-05-10T12:52:06.188Z Has data issue: false hasContentIssue false
  • English
  • Français

COINTEGRATION FOR PERIODICALLY INTEGRATED PROCESSES

Published online by Cambridge University Press:  06 September 2007

Tomás del Barrio Castro  and
Denise R. Osborn
Tomás del Barrio Castro
Affiliation:
University of Barcelona
Denise R. Osborn
Affiliation:
University of Manchester
Get access Rights & Permissions [Opens in a new window]

Abstract

Integration for seasonal time series can take the form of seasonal periodic or nonperiodic integration. When seasonal time series are periodically integrated, we show that any cointegration is either full periodic cointegration or full nonperiodic cointegration, with no possibility of cointegration applying for only some seasons. In contrast, seasonally integrated series can be seasonally, periodically or nonperiodically cointegrated, with the possibility of cointegration applying for a subset of seasons. Cointegration tests are analyzed for periodically integrated series. A residual-based test is examined, and its asymptotic distribution is derived under the null hypothesis of no cointegration. A Monte Carlo analysis shows good performance in terms of size and power. The role of deterministic terms in the cointegrating test regression is also investigated. Further, we show that the asymptotic distribution of the error-correction test for periodic cointegration derived by Boswijk and Franses (1995, Review of Economics and Statistics 77, 436–454) does not apply for periodically integrated processes.The authors gratefully acknowledge the comments of participants at the conference on Unit Root and Cointegration Testing, University of the Algave, September–October 2005, and they particularly thank two anonymous referees and Helmut Lütkepohl (co-editor of this issue of Econometric Theory) for their constructive comments, which have substantially improved the generality of the results in the paper. Tomás del Barrio Castro acknowledges financial support from Ministerio de Educación y Ciencia SEJ2005-07781/ECON.

Information

Type
Research Article
Information
Econometric Theory , Volume 24 , Issue 1 , February 2008 , pp. 109 - 142
Copyright
© 2008 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.)

Article purchase

Temporarily unavailable

References

REFERENCES

Birchenhall, C.R., R.C. Bladen-Hovell, A.P.L. Chui, D.R. Osborn, & J.P. Smith (1989) A seasonal model of consumption. Economic Journal 99, 837–843.Google Scholar
Boswijk, H.P. (1994) Testing for an unstable root in conditional and structural error correction models. Journal of Econometrics 63, 37–60.Google Scholar
Boswijk, H.P. & P.H. Franses (1995) Periodic cointegration: Representation and inference. Review of Economics and Statistics 77, 436–454.Google Scholar
Boswijk, H.P. & P.H. Franses (1996) Unit roots in periodic autoregression. Journal of Time Series Analysis 17, 221–245.Google Scholar
Cubadda, G. (2001) Complex reduced rank models for seasonally cointegrated time series. Oxford Bulletin of Economics and Statistics 63, 497–511.Google Scholar
Engle, R.F. & C.W.J. Granger (1987) Cointegration and error correction: Representation, estimation and testing. Econometrica 55, 251–276.Google Scholar
Engle, R.F., C.W.J. Granger, S. Hylleberg, & H.S. Lee (1993) Seasonal cointegration: The Japanese consumption function. Journal of Econometrics 55, 275–303.Google Scholar
Franses, P.H. (1993) A method to select between periodic cointegration and seasonal cointegration. Economics Letters 41, 7–10.Google Scholar
Franses, P.H. (1994) A multivariate approach to modelling univariate seasonal time series. Journal of Econometrics 63, 133–151.Google Scholar
Franses, P.H. (1995) A vector of quarters representation for bivariate time series. Econometric Reviews 14, 55–63.Google Scholar
Franses, P.H. (1996) Periodicity and Stochastic Trends in Economic Time Series. Oxford University Press.
Franses, P.H. & T. Kloek (1995) A periodic cointegration model of quarterly consumption. Applied Stochastic Models and Data Analysis 11, 159–166.Google Scholar
Ghysels, E. & D.R. Osborn (2001) The Econometric Analysis of Seasonal Time Series. Cambridge University Press.
Haldrup, N., S. Hylleberg, G. Pons, & A. Sansó (2007) Common periodic correlation features and the interaction of stocks and flows in daily airport data. Journal of Business & Economic Statistics 25, 21–32.Google Scholar
Hansen, B. (1992) Efficient estimation and testing of cointegration vectors in the presence of deterministic trends. Journal of Econometrics 53, 87–121.Google Scholar
Hylleberg, S., R.F. Engle, C.W.J. Granger, & B.S. Yoo (1990) Seasonal integration and cointegration. Journal of Econometrics 44, 215–238.Google Scholar
Johansen, S. & E. Schaumburg (1999) Likelihood analysis of seasonal cointegration. Journal of Econometrics 88, 301–339.Google Scholar
Kleibergen, F. & P.H. Franses (1999) Cointegration in a Periodic Autoregression. Econometric Institute Report EI-9906/A, Erasmus University of Rotterdam.
Lee, H.S. (1992) Maximum likelihood inference on cointegration and seasonal cointegration. Journal of Econometrics 54, 1–49.Google Scholar
Löf, M. & P.H. Franses (2001) On forecasting seasonal cointegrated time series. International Journal of Forecasting 17, 601–621.Google Scholar
Osborn, D.R. (1991) The implications of periodically varying coefficients for Seasonal Time Series Processes. Journal of Econometrics 48, 373–384.Google Scholar
Osborn, D.R. (2002) Cointegration for Seasonal Time Series Processes. Mimeo, University of Manchester.
Paap, R. & P.H. Franses (1999) On trends and constants in periodic autoregressions. Econometric Reviews 18, 271–286.Google Scholar
Phillips, P.C.B. & S.N. Durlauf (1986) Multiple time series regression with integrated processes. Review of Economic Studies 53, 473–495.Google Scholar
Phillips, P.C.B. & S. Ouliaris (1990) Asymptotic properties of residual based tests for cointegration. Econometrica 58, 165–193.Google Scholar