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Cointegration, root functions and minimal bases

Author

Listed:
  • Massimo Franchi

    ("Sapienza" University of Rome)

  • Paolo Paruolo

    (European Commission, Joint Research Centre)

Abstract

This paper discusses the concept of cointegrating space for systems integrated of order higher than 1. It is first observed that the notions of (polynomial) cointegrating vectors and of root functions coincide. Second, the cointegrating space is defined as a subspace of the space of rational vectors. Third, it is shown that canonical sets of root functions can be used to generate a basis of the cointegrating space. Fourth, results on how to reduce bases of rational vector spaces to polynomial bases with minimal order (i.e. minimal bases) are shown to imply the separation of cointegrating vectors that potentially do not involve differences of the process from the ones that require them. Finally, it is argued that minimality of polynomial bases and economic identification of cointegrating vectors can be properly combined.

Suggested Citation

  • Massimo Franchi & Paolo Paruolo, 2019. "Cointegration, root functions and minimal bases," DSS Empirical Economics and Econometrics Working Papers Series 2019/2, Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome.
    • Handle: RePEc:sas:wpaper:20192
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    References listed on IDEAS

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    4. Beare, Brendan K. & Seo, Won-Ki, 2020. "Representation Of I(1) And I(2) Autoregressive Hilbertian Processes," Econometric Theory, Cambridge University Press, vol. 36(5), pages 773-802, October.
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    7. Massimo Franchi & Paolo Paruolo, 2019. "A general inversion theorem for cointegration," Econometric Reviews, Taylor & Francis Journals, vol. 38(10), pages 1176-1201, November.
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    More about this item

    Keywords

    VAR; Cointegration; I(d); Vector spaces.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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