COINTEGRATION FOR PERIODICALLY INTEGRATED PROCESSES

Tomás del Barrio Castro () and Denise Osborn ()

Econometric Theory, 2008, vol. 24, issue 01, pages 109-142

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 L tkepohl (co-editor of this issue of Econometric Theory) for their constructive comments, which have substantially improved the generality of the results in the paper. Tom s del Barrio Castro acknowledges financial support from Ministerio de Educaci n y Ciencia SEJ2005-07781 ECON.

Date: 2008

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Working Paper: Cointegration for Periodically Integrated Processes (2005)
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