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Strongly Consistent Determination of Cointegrating Rank via Canonical Correlations

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  • Poskitt, Don S

Abstract

This article is concerned with the statistical analysis of nonstationary, cointegrated time series. The estimation of the cointegrating structure of such time series is considered, and the problem of identifying the cointegrating rank is addressed. A methodology is presented that leads to strongly consistent estimates of this quantity. The identification is based on a canonical correlation analysis of the original variables and presents an alternative approach to those currently in vogue. The procedures are easily implemented and the practical relevance of the results obtained, which are founded on asymptotic theory, is demonstrated by means of a small simulation study.

Suggested Citation

  • Poskitt, Don S, 2000. "Strongly Consistent Determination of Cointegrating Rank via Canonical Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(1), pages 77-90, January.
    • Handle: RePEc:bes:jnlbes:v:18:y:2000:i:1:p:77-90
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    Cited by:

    1. M. Atikur Rahman Khan & D.S. Poskitt, 2014. "On The Theory and Practice of Singular Spectrum Analysis Forecasting," Monash Econometrics and Business Statistics Working Papers 3/14, Monash University, Department of Econometrics and Business Statistics.
    2. D. S. Poskitt, 2004. "On The Identification and Estimation of Partially Nonstationary ARMAX Systems," Monash Econometrics and Business Statistics Working Papers 20/04, Monash University, Department of Econometrics and Business Statistics.
    3. D.S. Poskitt & Wenying Yao, 2012. "VAR Modeling and Business Cycle Analysis: A Taxonomy of Errors," Monash Econometrics and Business Statistics Working Papers 11/12, Monash University, Department of Econometrics and Business Statistics.
    4. George Athanasopoulos & Donald S. Poskitt & Farshid Vahid & Wenying Yao, 2016. "Determination of Long‐run and Short‐run Dynamics in EC‐VARMA Models via Canonical Correlations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(6), pages 1100-1119, September.
    5. Al-Sadoon, Majid M., 2014. "Geometric and long run aspects of Granger causality," Journal of Econometrics, Elsevier, vol. 178(P3), pages 558-568.
    6. Bauer, Dietmar & Wagner, Martin, 2002. "Estimating cointegrated systems using subspace algorithms," Journal of Econometrics, Elsevier, vol. 111(1), pages 47-84, November.
    7. Koo, Bonsoo & Anderson, Heather M. & Seo, Myung Hwan & Yao, Wenying, 2020. "High-dimensional predictive regression in the presence of cointegration," Journal of Econometrics, Elsevier, vol. 219(2), pages 456-477.
    8. D.S. Poskitt, 2009. "Vector Autoregresive Moving Average Identification for Macroeconomic Modeling: Algorithms and Theory," Monash Econometrics and Business Statistics Working Papers 12/09, Monash University, Department of Econometrics and Business Statistics.
    9. George Kapetanios, 2003. "A New Nonparametric Test of Cointegration Rank," Working Papers 482, Queen Mary University of London, School of Economics and Finance.
    10. Kirstin Hubrich & Helmut Lutkepohl & Pentti Saikkonen, 2001. "A Review Of Systems Cointegration Tests," Econometric Reviews, Taylor & Francis Journals, vol. 20(3), pages 247-318.
    11. Alfredo Garcia Hiernaux & Miguel Jerez & José Casals, 2005. "Unit Roots and Cointegrating Matrix Estimation using Subspace Methods," Documentos de Trabajo del ICAE 0512, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    12. D. S. Poskitt, 2005. "Autoregressive Approximation in Nonstandard Situations: The Non-Invertible and Fractionally Integrated Cases," Monash Econometrics and Business Statistics Working Papers 16/05, Monash University, Department of Econometrics and Business Statistics.
    13. Md Atikur Rahman Khan & D.S. Poskitt, 2011. "Window Length Selection and Signal-Noise Separation and Reconstruction in Singular Spectrum Analysis," Monash Econometrics and Business Statistics Working Papers 23/11, Monash University, Department of Econometrics and Business Statistics.
    14. Alfredo García Hiernaux & Miguel Jerez & José Casals, 2005. "Deteccióon de Raíces Unitarias y Cointegración mediante Métodos de Subespacios," Documentos de Trabajo del ICAE 0503, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    15. George Kapetanios, 2003. "A New Nonparametric Test of Cointegration Rank," Working Papers 482, Queen Mary University of London, School of Economics and Finance.
    16. D. Poskitt, 2007. "Autoregressive approximation in nonstandard situations: the fractionally integrated and non-invertible cases," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(4), pages 697-725, December.
    17. Athanasopouolos, George & Poskitt, Don & Vahid, Farshid & Yao, Wenying, 2014. "Forecasting with EC-VARMA models," Working Papers 2014-07, University of Tasmania, Tasmanian School of Business and Economics, revised 22 Feb 2014.
    18. D.S. Poskitt, 2016. "Singular Spectrum Analysis of Grenander Processes and Sequential Time Series Reconstruction," Monash Econometrics and Business Statistics Working Papers 15/16, Monash University, Department of Econometrics and Business Statistics.
    19. Martin Wagner, 2004. "A Comparison of Johansen's, Bierens’ and the Subspace Algorithm Method for Cointegration Analysis," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 66(3), pages 399-424, July.
    20. Khan, M. Atikur Rahman & Poskitt, D.S., 2017. "Forecasting stochastic processes using singular spectrum analysis: Aspects of the theory and application," International Journal of Forecasting, Elsevier, vol. 33(1), pages 199-213.
    21. Guillermo Carlomagno & Antoni Espasa, 2021. "Discovering Specific Common Trends in a Large Set of Disaggregates: Statistical Procedures, their Properties and an Empirical Application," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(3), pages 641-662, June.
    22. Poskitt, D. S., 2003. "On the specification of cointegrated autoregressive moving-average forecasting systems," International Journal of Forecasting, Elsevier, vol. 19(3), pages 503-519.
    23. Heaney, Richard, 2002. "Does knowledge of the cost of carry model improve commodity futures price forecasting ability?: A case study using the London Metal Exchange lead contract," International Journal of Forecasting, Elsevier, vol. 18(1), pages 45-65.
    24. Poskitt, D.S., 2016. "Vector autoregressive moving average identification for macroeconomic modeling: A new methodology," Journal of Econometrics, Elsevier, vol. 192(2), pages 468-484.

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