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Complex Reduced Rank Models For Seasonally Cointegrated Time Series

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  • Gianluca Cubadda

Abstract

This paper introduces a new representation for seasonally cointegrated variables, namely the complex error correction model, which allows statistical inference to be performed by reduced rank regression. The suggested estimators and tests statistics are asymptotically equivalent to their maximum likelihood counterparts. The small sample properties are evaluated by a Monte Carlo study and an empirical example is presented to illustrate the concepts and methods.

Suggested Citation

  • Gianluca Cubadda, 2001. "Complex Reduced Rank Models For Seasonally Cointegrated Time Series," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 63(4), pages 497-511, September.
    • Handle: RePEc:bla:obuest:v:63:y:2001:i:4:p:497-511
    DOI: 10.1111/1468-0084.00231
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    Cited by:

    1. Cubadda, Gianluca & Omtzigt, Pieter, 2005. "Small-sample improvements in the statistical analysis of seasonally cointegrated systems," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 333-348, April.
    2. Marco Centoni & Gianluca Cubadda, 2011. "Modelling comovements of economic time series: a selective survey," Statistica, Department of Statistics, University of Bologna, vol. 71(2), pages 267-294.
    3. Tomás del Barrio Castro & Gianluca Cubadda & Denise R. Osborn, 2022. "On cointegration for processes integrated at different frequencies," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 412-435, May.
    4. Svend Hylleberg, 2006. "Seasonal Adjustment," Economics Working Papers 2006-04, Department of Economics and Business Economics, Aarhus University.
    5. Ozlem Tasseven, 2009. "Seasonal Co-integration An Extension of the Johansen and Schaumburg Approach with an Exclusion Test," Panoeconomicus, Savez ekonomista Vojvodine, Novi Sad, Serbia, vol. 56(1), pages 39-53, March.
    6. Seong, Byeongchan, 2009. "Bonferroni correction for seasonal cointegrating ranks," Economics Letters, Elsevier, vol. 103(1), pages 42-44, April.
    7. Wróblewska, Justyna, 2025. "Bayesian analysis of seasonally cointegrated VAR models," Econometrics and Statistics, Elsevier, vol. 35(C), pages 55-70.
    8. Domenico Depalo, 2009. "A seasonal unit-root test with Stata," Stata Journal, StataCorp LLC, vol. 9(3), pages 422-438, September.
    9. Bertrand Candelon & Gianluca Cubadda, 2006. "Testing for Parameter Stability in Dynamic Models across Frequencies," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(s1), pages 741-760, December.
    10. Philip Kostov & John Lingard, 2005. "Seasonally specific model analysis of UK cereals prices," Econometrics 0507014, University Library of Munich, Germany.
    11. Darne, Olivier, 2004. "Seasonal cointegration for monthly data," Economics Letters, Elsevier, vol. 82(3), pages 349-356, March.
    12. Gil-Alana, L.A., 2008. "Testing of seasonal integration and cointegration with fractionally integrated techniques: An application to the Danish labour demand," Economic Modelling, Elsevier, vol. 25(2), pages 326-339, March.
    13. Sung K. Ahn & Sinsup Cho & B. Chan Seong, 2004. "Inference of Seasonal Cointegration: Gaussian Reduced Rank Estimation and Tests for Various Types of Cointegration," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 66(2), pages 261-284, May.
    14. Bauer, Dietmar & del Barrio Castro, Tomás, 2025. "The Effect of Aggregation on Seasonal Cointegration in Mixed Frequency data," MPRA Paper 126066, University Library of Munich, Germany.
    15. Nyblom, Jukka & Suomala, Jaakko, 2014. "Tests for real and complex unit roots in vector autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 224-239.
    16. Seong, Byeongchan, 2013. "Semiparametric selection of seasonal cointegrating ranks using information criteria," Economics Letters, Elsevier, vol. 120(3), pages 592-595.
    17. Fabio Busetti, 2006. "Tests of seasonal integration and cointegration in multivariate unobserved component models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(4), pages 419-438.

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