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Maximum likelihood estimation of fractionally cointegrated systems

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  • Katarzyna Lasak

    ()
    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

Abstract

In this paper we consider a fractionally cointegrated error correction model and investigate asymptotic properties of the maximum likelihood (ML) estimators of the matrix of the cointe- gration relations, the degree of fractional cointegration, the matrix of the speed of adjustment to the equilibrium parameters and the variance-covariance matrix of the error term. We show that using ML principles to estimate jointly all parameters of the fractionally cointegrated system we obtain consistent estimates and provide their asymptotic distributions. The cointegration matrix is asymptotically mixed normal distributed, while the degree of fracional cointegration and the speed of adjustment to the equilibrium matrix have joint normal distribution, which proves the intuition that the memory of the cointegrating residuals affects the speed of conver- gence to the long-run equilibrium, but does not have any influence on the long-run relationship. The rate of convergence of the estimators of the long-run relationships depends on the coin- tegration degree but it is optimal for the strong cointegration case considered. We also prove that misspecification of the degree of fractional cointegation does not affect the consistency of the estimators of the cointegration relationships, although usual inference rules are not valid. We illustrate our results in finite samples by Monte Carlo analysis.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2008-53.

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Length: 37
Date of creation: 12 Sep 2008
Date of revision:
Handle: RePEc:aah:create:2008-53

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Web page: http://www.econ.au.dk/afn/

Related research

Keywords: Error correction model; Gaussian VAR model; Maximum likelihood estimation; Fractional cointegration;

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Citations

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Cited by:
  1. Caporin, Massimiliano & Ranaldo, Angelo & Santucci de Magistris, Paolo, 2013. "On the predictability of stock prices: A case for high and low prices," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5132-5146.
  2. Eduardo Rossi & Paolo Santucci de Magistris, 2009. "A No Arbitrage Fractional Cointegration Analysis Of The Range Based Volatility," CREATES Research Papers 2009-31, School of Economics and Management, University of Aarhus.
  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. Federico Carlini & Katarzyna Lasak, 2014. "On an Estimation Method for an Alternative Fractionally Cointegrated Model," Tinbergen Institute Discussion Papers 14-052/III, Tinbergen Institute.
  5. Marcel Aloy & Gilles De Truchis, 2012. "Estimation and Testing for Fractional Cointegration," Working Papers halshs-00793206, HAL.
  6. Lasak, Katarzyna, 2010. "Likelihood based testing for no fractional cointegration," Journal of Econometrics, Elsevier, vol. 158(1), pages 67-77, September.
  7. Søren Johansen, 2011. "An extension of cointegration to fractional autoregressive processes," CREATES Research Papers 2011-06, School of Economics and Management, University of Aarhus.

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