No CrossRef data available.
Article contents
COINTEGRATION FOR PERIODICALLY INTEGRATED PROCESSES
Published online by Cambridge University Press: 06 September 2007
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.
- Type
- Research Article
- Information
- Copyright
- © 2008 Cambridge University Press
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