# The role of initial values in nonstationary fractional time series models

## Author Info

Listed author(s):
• Søren Johansen

()

(University of Copenhagen and CREATES)

• Morten Ørregaard Nielsen

()

(Queen?s University and CREATES)

## Abstract

We consider the nonstationary fractional model $\Delta^{d}X_{t}=\varepsilon _{t}$ with $\varepsilon_{t}$ i.i.d.$(0,\sigma^{2})$ and $d>1/2$. We derive an analytical expression for the main term of the asymptotic bias of the maximum likelihood estimator of $d$ conditional on initial values, and we discuss the 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: ftp://ftp.econ.au.dk/creates/rp/12/rp12_47.pdf

## Bibliographic Info

Paper provided by Department of Economics and Business Economics, Aarhus University in its series CREATES Research Papers with number 2012-47.

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 Length: 29 Date of creation: 08 Nov 2012 Handle: RePEc:aah:create:2012-47 Contact details of provider: Web page: http://www.econ.au.dk/afn/

## References

References listed on IDEAS
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1. Søren Johansen & Morten Ørregaard Nielsen, 2007. "Likelihood inference for a nonstationary fractional autoregressive model," CREATES Research Papers 2007-33, Department of Economics and Business Economics, Aarhus University.
2. 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.
3. Søren Johansen & Morten Ørregaard Nielsen, 2010. "Likelihood inference for a fractionally cointegrated vector autoregressive model," CREATES Research Papers 2010-24, Department of Economics and Business Economics, Aarhus University.
4. Morten Ørregaard Nielsen, 2014. "Asymptotics for the conditional-sum-of-squares estimator in multivariate fractional time series models," CREATES Research Papers 2014-34, Department of Economics and Business Economics, Aarhus University.
5. Tschernig, Rolf & Weber, Enzo & Weigand, Roland, 2010. "Long-run Identification in a Fractionally Integrated System," University of Regensburg Working Papers in Business, Economics and Management Information Systems 447, University of Regensburg, Department of Economics.
6. 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.
7. 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.
8. Donald W.K. Andrews & Offer Lieberman, 2002. "Higher-order Improvements of the Parametric Bootstrap for Long-memory Gaussian Processes," Cowles Foundation Discussion Papers 1378, Cowles Foundation for Research in Economics, Yale University.
9. 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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