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A characterization of vector autoregressive processes with common cyclical features

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  • Franchi, Massimo
  • Paruolo, Paolo

Abstract

This paper presents necessary and sufficient conditions for the existence of common cyclical features in Vector Auto Regressive (VAR) processes integrated of order 0, 1, 2, where the common cyclical features correspond to common serial correlation (CS), commonality in the final equations (CE) and co-dependence (CD). The results are based on local rank factorizations of the reversed AR polynomial around the poles of its inverse. All processes with CS structures are found to present also CE structures and vice versa. The presence of CD structures, instead, implies the presence of both CS and CE structures, but not vice versa. Characterizations of the CS, CE, CD linear combinations are given in terms of linear subspaces defined in the local rank factorizations.

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  • 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.
    • Handle: RePEc:eee:econom:v:163:y:2011:i:1:p:105-117
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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. Gianluca Cubadda & Alain Hecq, 2021. "Reduced Rank Regression Models in Economics and Finance," CEIS Research Paper 525, Tor Vergata University, CEIS, revised 08 Nov 2021.
    3. Massimo Franchi & Paolo Paruolo, 2015. "Minimality of State Space Solutions of DSGE Models and Existence Conditions for Their VAR Representation," Computational Economics, Springer;Society for Computational Economics, vol. 46(4), pages 613-626, December.
    4. Marco Centoni & Gianluca Cubadda, 2015. "Common Feature Analysis of Economic Time Series: An Overview and Recent Developments," CEIS Research Paper 355, Tor Vergata University, CEIS, revised 05 Oct 2015.
    5. Carsten Trenkler & Enzo Weber, 2013. "Codependent VAR models and the pseudo-structural form," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(3), pages 287-295, July.
    6. S. Yaser Samadi & Wiranthe B. Herath, 2023. "Reduced-rank Envelope Vector Autoregressive Models," Papers 2309.12902, arXiv.org.
    7. Marcel Gorenflo, 2013. "Futures price dynamics of CO 2 emission allowances," Empirical Economics, Springer, vol. 45(3), pages 1025-1047, December.
    8. Swensen, Anders Rygh, 2011. "A bootstrap algorithm for testing cointegration rank in VAR models in the presence of stationary variables," Journal of Econometrics, Elsevier, vol. 165(2), pages 152-162.
    9. Carsten Trenkler & Enzo Weber, 2013. "Testing for codependence of cointegrated variables," Applied Economics, Taylor & Francis Journals, vol. 45(15), pages 1953-1964, May.

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