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The role of initial values in nonstationary fractional time series models

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  • Søren Johansen

    (University of Copenhagen and CREATES)

  • Morten Ørregaard Nielsen

    (Queen's University and CREATES)

Abstract

We consider the nonstationary fractional model Delta^d Xt = epsilon t with epsilon t i.i.d.(0;sigma^2) and d > 1/2. We derive an analytical expression for the main term of the asymptotic biasof the maximum likelihood estimator of d conditional on initial values, and we discussthe role of the initial values for the bias. The results are partially extended to other fractional models, and three different applications of the theoretical results are given.

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Bibliographic Info

Paper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 12-18.

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Length: 30 pages
Date of creation: 08 Nov 2012
Date of revision:
Handle: RePEc:kud:kuiedp:1218

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Keywords: Asymptotic expansion; bias; conditional inference; fractional integration; initial values; likelihood inference;

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  1. Rolf Tschernig & Enzo Weber & Roland Weigand, 2013. "Long-Run Identification in a Fractionally Integrated System," Journal of Business & Economic Statistics, Taylor & Francis Journals, Taylor & Francis Journals, vol. 31(4), pages 438-450, October.
  2. Søren Johansen & Morten Ørregaard Nielsen, 2010. "Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model," Discussion Papers 10-15, University of Copenhagen. Department of Economics.
  3. Eduardo Rossi & Paolo Santucci de Magistris, 2013. "A No‐Arbitrage Fractional Cointegration Model for Futures and Spot Daily Ranges," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 33(1), pages 77-102, 01.
  4. Søren Johansen & Morten Ørregaard Nielsen, 2010. "Likelihood inference for a nonstationary fractional autoregressive model," Working Papers, Queen's University, Department of Economics 1172, Queen's University, Department of Economics.
  5. David Byers & James Davidson & David Peel, 1997. "Modelling Political Popularity: an Analysis of Long-range Dependence in Opinion Poll Series," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 160(3), pages 471-490.
  6. Juan J. Dolado & Jesus Gonzalo & Laura Mayoral, 2002. "A Fractional Dickey-Fuller Test for Unit Roots," Econometrica, Econometric Society, Econometric Society, vol. 70(5), pages 1963-2006, September.
  7. Morten Ørregaard Nielsen, 2011. "Asymptotics for the conditional-sum-of-squares estimator in multivariate fractional time series models," Working Papers, Queen's University, Department of Economics 1259, Queen's University, Department of Economics.
  8. Johansen, SØren, 2008. "A Representation Theory For A Class Of Vector Autoregressive Models For Fractional Processes," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 24(03), pages 651-676, June.
  9. Donald W.K. Andrews & Offer Lieberman, 2002. "Higher-order Improvements of the Parametric Bootstrap for Long-memory Gaussian Processes," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1378, Cowles Foundation for Research in Economics, Yale University.
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Cited by:
  1. Bent Jesper Christensen & Robinson Kruse & Philipp Sibbertsen, 2013. "A unified framework for testing in the linear regression model under unknown order of fractional integration," CREATES Research Papers 2013-35, School of Economics and Management, University of Aarhus.
  2. Eduardo Rossi & Paolo Santucci de Magistris, 2009. "Long Memory and Tail dependence in Trading Volume and Volatility," CREATES Research Papers 2009-30, School of Economics and Management, University of Aarhus.

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