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The role of initial values in nonstationary fractional time series models

  • Søren Johansen

    (University of Copenhagen and CREATES)

  • Morten Ørregaard Nielsen

    (Queen's University and CREATES)

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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File URL: http://www.econ.ku.dk/english/research/publications/wp/dp_2012/1218.pdf
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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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  1. 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.
  2. Søren Johansen & Morten Ørregaard Nielsen, 2010. "Likelihood inference for a nonstationary fractional autoregressive model," Working Papers 1172, Queen's University, Department of Economics.
  3. Rolf Tschernig & Enzo Weber & Roland Weigand, 2013. "Long-Run Identification in a Fractionally Integrated System," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(4), pages 438-450, October.
  4. 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.
  5. 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.
  6. Andrews, Donald W.K. & Lieberman, Offer & Marmer, Vadim, 2006. "Higher-order improvements of the parametric bootstrap for long-memory Gaussian processes," Journal of Econometrics, Elsevier, vol. 133(2), pages 673-702, August.
  7. 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.
  8. Morten Ørregaard Nielsen, 2015. "Asymptotics for the Conditional-Sum-of-Squares Estimator in Multivariate Fractional Time-Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 154-188, 03.
  9. Juan J. Dolado & Jesus Gonzalo & Laura Mayoral, 2002. "A Fractional Dickey-Fuller Test for Unit Roots," Econometrica, Econometric Society, vol. 70(5), pages 1963-2006, September.
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