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An extension of cointegration to fractional autoregressive processes

  • Søren Johansen

    ()

    (University of Copenhagen and CREATES)

This paper contains an overview of some recent results on the statistical analysis of cofractional processes, see Johansen and Nielsen (2010). We first give an brief summary of the analysis of cointegration in the vector autoregressive model and then show how this can be extended to fractional processes. The model allows the process X(t) to be fractional of order d and cofractional of order d-b>0; that is, there exist vectors beta for which beta'X(t) is fractional of order d-b. We analyse the Gaussian likelihood function to derive estimators and test statistics. The asymptotic properties are derived without the Gaussian assumption, under suitable moment conditions. We assume that the initial values are bounded and show that they do not influence the asymptotic analysis The estimator of \beta is asymptotically mixed Gaussian and estimators of the remaining parameters are asymptotically Gaussian. The asymptotic distribution of the likelihood ratio test for cointegration rank is a functional of fractional Brownian motion.

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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2011-06.

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Length: 15
Date of creation: 31 Jan 2011
Date of revision:
Handle: RePEc:aah:create:2011-06
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  1. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November.
  2. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
  3. Johansen, Søren & Nielsen, Morten Ørregaard, 2010. "Likelihood inference for a nonstationary fractional autoregressive model," Journal of Econometrics, Elsevier, vol. 158(1), pages 51-66, September.
  4. Hualde, J. & Robinson, P.M., 2010. "Semiparametric inference in multivariate fractionally cointegrated systems," Journal of Econometrics, Elsevier, vol. 157(2), pages 492-511, August.
  5. Campbell, John & Shiller, Robert, 1987. "Cointegration and Tests of Present Value Models," Scholarly Articles 3122490, Harvard University Department of Economics.
  6. Johansen, Soren, 1995. "The Role of Ancillarity in Inference for Non-stationary Variables," Economic Journal, Royal Economic Society, vol. 105(429), pages 302-20, March.
  7. Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers 2008-53, School of Economics and Management, University of Aarhus.
  8. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  9. Granger, Clive W J, 1986. "Developments in the Study of Cointegrated Economic Variables," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 213-28, August.
  10. Katarzyna Lasak, 2008. "Likelihood based testing for no fractional cointegration," CREATES Research Papers 2008-52, School of Economics and Management, University of Aarhus.
  11. Peter M. Robinson & Javier Hualde, 2002. "Cointegration in Fractional Systems with Unknown Integration Orders," Faculty Working Papers 07/02, School of Economics and Business Administration, University of Navarra.
  12. Jeganathan, P., 1999. "On Asymptotic Inference In Cointegrated Time Series With Fractionally Integrated Errors," Econometric Theory, Cambridge University Press, vol. 15(04), pages 583-621, August.
  13. M. Ruth & K. Donaghy & P. Kirshen, 2006. "Introduction," Chapters, in: Regional Climate Change and Variability, chapter 1 Edward Elgar.
  14. Juselius, Katarina, 2006. "The Cointegrated VAR Model: Methodology and Applications," OUP Catalogue, Oxford University Press, number 9780199285679, March.
  15. Johansen, SØren, 2008. "A Representation Theory For A Class Of Vector Autoregressive Models For Fractional Processes," Econometric Theory, Cambridge University Press, vol. 24(03), pages 651-676, June.
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