Advanced Search
MyIDEAS: Login to save this article or follow this journal

Likelihood inference for a nonstationary fractional autoregressive model

Contents:

Author Info

  • Johansen, Søren
  • Nielsen, Morten Ørregaard

Abstract

This paper discusses model-based inference in an autoregressive model for fractional processes which allows the process to be fractional of order d or d-b. Fractional differencing involves infinitely many past values and because we are interested in nonstationary processes we model the data X1,...,XT given the initial values , as is usually done. The initial values are not modeled but assumed to be bounded. This represents a considerable generalization relative to previous work where it is assumed that initial values are zero. For the statistical analysis we assume the conditional Gaussian likelihood and for the probability analysis we also condition on initial values but assume that the errors in the autoregressive model are i.i.d. with suitable moment conditions. We analyze the conditional likelihood and its derivatives as stochastic processes in the parameters, including d and b, and prove that they converge in distribution. We use these results to prove consistency of the maximum likelihood estimator for d,b in a large compact subset of {1/2

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.sciencedirect.com/science/article/B6VC0-4YKGJBK-1/2/44a2310521f1ced5e546ca1c2db81889
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 158 (2010)
Issue (Month): 1 (September)
Pages: 51-66

as in new window
Handle: RePEc:eee:econom:v:158:y:2010:i:1:p:51-66

Contact details of provider:
Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Dickey-Fuller test Fractional unit root Likelihood inference;

Other versions of this item:

Find related papers by JEL classification:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. 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.
  2. Sowell, Fallaw, 1990. "The Fractional Unit Root Distribution," Econometrica, Econometric Society, vol. 58(2), pages 495-505, March.
  3. Ling, Shiqing & Li, W.K., 2001. "Asymptotic Inference For Nonstationary Fractionally Integrated Autoregressive Moving-Average Models," Econometric Theory, Cambridge University Press, vol. 17(04), pages 738-764, August.
  4. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(02), pages 241-257, June.
  5. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
  6. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(04), pages 549-582, August.
  7. Ignacio N Lobato & Carlos Velasco, 2007. "Efficient Wald Tests for Fractional Unit Roots," Econometrica, Econometric Society, vol. 75(2), pages 575-589, 03.
  8. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
  9. Nielsen, Morten rregaard, 2004. "Efficient Likelihood Inference In Nonstationary Univariate Models," Econometric Theory, Cambridge University Press, vol. 20(01), pages 116-146, February.
  10. repec:cup:cbooks:9780521496032 is not listed on IDEAS
  11. Newey, Whitney K, 1991. "Uniform Convergence in Probability and Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 59(4), pages 1161-67, July.
  12. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January.
  13. 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.
  14. Marinucci, D. & Robinson, P. M., 2000. "Weak convergence of multivariate fractional processes," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 103-120, March.
  15. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
  16. 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.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Tschernig, Rolf & Weber, Enzo & Weigand, Roland, 2013. "Fractionally Integrated VAR Models with a Fractional Lag Operator and Deterministic Trends: Finite Sample Identification and Two-step Estimation," University of Regensburg Working Papers in Business, Economics and Management Information Systems 471, University of Regensburg, Department of Economics.
  2. Giuseppe Cavaliere & Morten Ørregaard Nielsen & A.M. Robert Taylor, 2014. "Bootstrap Score Tests for Fractional Integration in Heteroskedastic ARFIMA Models, with an Application to Price Dynamics in Commodity Spot and Futures Markets," CREATES Research Papers 2014-22, School of Economics and Management, University of Aarhus.
  3. Morten Ørregaard Nielsen, 2008. "Nonparametric Cointegration Analysis of Fractional Systems With Unknown Integration Orders," Working Papers 1174, Queen's University, Department of Economics.
  4. Søren Johansen & Morten Ørregaard Nielsen, 2012. "The role of initial values in nonstationary fractional time series models," Discussion Papers 12-18, University of Copenhagen. Department of Economics.
  5. Søren Johansen, 2010. "An Extension of Cointegration to Fractional Autoregressive Processes," Discussion Papers 10-28, University of Copenhagen. Department of Economics.
  6. Luis Gil-Alana & Antonio Moreno, 2012. "Fractional integration and structural breaks in U.S. macro dynamics," Empirical Economics, Springer, vol. 43(1), pages 427-446, August.
  7. Niels Haldrup & Robinson Kruse, 2014. "Discriminating between fractional integration and spurious long memory," CREATES Research Papers 2014-19, School of Economics and Management, University of Aarhus.
  8. Maggie E.C. Jones & Morten Ørregaard Nielsen & Michal Ksawery Popiel, 2014. "A fractionally cointegrated VAR analysis of economic voting and political support," Working Papers 1326, Queen's University, Department of Economics.
  9. James Davidson & Nigar Hashimzade, 2008. "Type I and Type II Fractional Brownian Motions: a Reconsideration," Discussion Papers 0816, Exeter University, Department of Economics.
  10. Giuseppe Cavaliere & Morten Ørregaard Nielsen & A. M. Robert Taylor, 2014. "Quasi-Maximum Likelihood Estimation of Heteroskedastic Fractional Time Series Models," Working Papers 1324, Queen's University, Department of Economics.
  11. Federico Carlini & Paolo Santucci de Magistris, 2013. "On the identification of fractionally cointegrated VAR models with the F(d) condition," CREATES Research Papers 2013-44, School of Economics and Management, University of Aarhus.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:158:y:2010:i:1:p:51-66. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.