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A Representation Theory For Polynomial Cofractionality In Vector Autoregressive Models

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  • Franchi, Massimo

Abstract

We extend the representation theory of the autoregressive model in the fractional lag operator of Johansen (2008, Econometric Theory 24, 651–676). A recursive algorithm for the characterization of cofractional relations and the corresponding adjustment coefficients is given, and it is shown under which condition the solution of the model is fractional of order d and displays cofractional relations of order d − b and polynomial cofractional relations of order d − 2 b ,…, d − cb ≥ 0 for integer c ; the cofractional relations and the corresponding moving average representation are characterized in terms of the autoregressive coefficients by the same algorithm. For c = 1 and c = 2 we find the results of Johansen (2008).

Suggested Citation

  • Franchi, Massimo, 2010. "A Representation Theory For Polynomial Cofractionality In Vector Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 26(04), pages 1201-1217, August.
  • Handle: RePEc:cup:etheor:v:26:y:2010:i:04:p:1201-1217_99
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    Cited by:

    1. Massimo Franchi & Paolo Paruolo, 2011. "Normal forms of regular matrix polynomials via local rank factorization," DSS Empirical Economics and Econometrics Working Papers Series 2011/1, Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome.
    2. Hualde, Javier, 2014. "Estimation of long-run parameters in unbalanced cointegration," Journal of Econometrics, Elsevier, vol. 178(2), pages 761-778.
    3. Franchi, Massimo & Paruolo, Paolo, 2011. "A characterization of vector autoregressive processes with common cyclical features," Journal of Econometrics, Elsevier, vol. 163(1), pages 105-117, July.
    4. Massimo Franchi, 2017. "On the structure of state space systems with unit roots," DSS Empirical Economics and Econometrics Working Papers Series 2017/4, Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome.
    5. Massimo Franchi & Paolo Paruolo, 2017. "A general inversion theorem for cointegration," DSS Empirical Economics and Econometrics Working Papers Series 2017/3, Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome.
    6. Paolo Santucci de Magistris & Federico Carlini, 2014. "On the identification of fractionally cointegrated VAR models with the F(d) condition," CREATES Research Papers 2014-43, Department of Economics and Business Economics, Aarhus University.

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