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Representation of Cointegrated Autoregressive Processes with Application to Fractional Processes

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  • S�ren Johansen

Abstract

We analyze vector autoregressive processes using the matrix valued characteristic polynomial. The purpose of this article is to give a survey of the mathematical results on inversion of a matrix polynomial in case there are unstable roots, to study integrated and cointegrated processes. The new results are in the I(2) representation, which contains explicit formulas for the first two terms and a useful property of the third. We define a new error correction model for fractional processes and derive a representation of the solution.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Econometric Reviews.

Volume (Year): 28 (2009)
Issue (Month): 1-3 ()
Pages: 121-145

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Handle: RePEc:taf:emetrv:v:28:y:2009:i:1-3:p:121-145

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Related research

Keywords: Error correction models; Fractional autoregressive model; Granger representation; Integration of order 1 and 2;

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Cited by:
  1. 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.
  2. de Truchis, Gilles, 2013. "Approximate Whittle analysis of fractional cointegration and the stock market synchronization issue," Economic Modelling, Elsevier, vol. 34(C), pages 98-105.
  3. Federico Carlini & Katarzyna Lasak, 2014. "On an Estimation Method for an Alternative Fractionally Cointegrated Model," CREATES Research Papers 2014-15, School of Economics and Management, University of Aarhus.
  4. Massimo Franchi & Paolo Paruolo, 2012. "On ABCs (and Ds) of VAR representations of DSGE models," DSS Empirical Economics and Econometrics Working Papers Series 2012/4, Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome.
  5. Johansen, Søren & Juselius, Katarina, 2014. "An asymptotic invariance property of the common trends under linear transformations of the data," Journal of Econometrics, Elsevier, vol. 178(P2), pages 310-315.
  6. Tim Bollerslev & Daniela Osterrieder & Natalia Sizova & George Tauchen, 2011. "Risk and Return: Long-Run Relationships, Fractional Cointegration, and Return Predictability," CREATES Research Papers 2011-51, School of Economics and Management, University of Aarhus.

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