Advanced Search
MyIDEAS: Login to save this paper or follow this series

Likelihood Inference for a Nonstationary Fractional Autoregressive Model

Contents:

Author Info

  • Søren Johansen

    (Department of Economics, University of Copenhagen)

  • Morten Ørregaard Nielsen

    (Cornell University)

Abstract

This paper discusses model based inference in an autoregressive model for fractional processes based on the Gaussian likelihood. The model allows for the process to be fractional of order d or d – b; where d ≥ b > 1/2 are parameters to be estimated. We model the data X, …, Xт given the initial values Xº-n, n = 0, 1, …, under the assumption that the errors are i.i.d. Gaussian. We consider the likelihood and its derivatives as stochastic processes in the parameters, and prove that they converge in distribution when the errors are i.i.d. with suitable moment conditions and the initial values are bounded. We use this to prove existence and consistency of the local likelihood estimator, and to find the asymptotic distribution of the estimators and the likelihood ratio test of the associated fractional unit root hypothesis, which contains the fractional Brownian motion of type II.

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.econ.ku.dk/english/research/publications/wp/2007/0727.pdf/
Download Restriction: no

Bibliographic Info

Paper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 07-27.

as in new window
Length: 43 pages
Date of creation: Aug 2007
Date of revision:
Handle: RePEc:kud:kuiedp:0727

Contact details of provider:
Postal: Øster Farimagsgade 5, Building 26, DK-1353 Copenhagen K., Denmark
Phone: (+45) 35 32 30 10
Fax: +45 35 32 30 00
Email:
Web page: http://www.econ.ku.dk
More information through EDIRC

Related research

Keywords: Dickey-Fuller test; fractional unit root; likelihood inference;

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

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 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.
  2. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(02), pages 241-257, June.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
  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. 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.
  10. Nielsen, Morten rregaard, 2004. "Efficient Likelihood Inference In Nonstationary Univariate Models," Econometric Theory, Cambridge University Press, vol. 20(01), pages 116-146, February.
  11. 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.
  12. Sowell, Fallaw, 1990. "The Fractional Unit Root Distribution," Econometrica, Econometric Society, vol. 58(2), pages 495-505, March.
  13. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(04), pages 549-582, August.
  14. Ignacio N Lobato & Carlos Velasco, 2007. "Efficient Wald Tests for Fractional Unit Roots," Econometrica, Econometric Society, vol. 75(2), pages 575-589, 03.
  15. repec:cup:cbooks:9780521496032 is not listed on IDEAS
  16. Newey, W.K., 1989. "Uniform Convergence In Probability And Stochastic Equicontinuity," Papers 342, Princeton, Department of Economics - Econometric Research Program.
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. 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.
  2. James Davidson & Nigar Hashimzade, 2008. "Type I and Type II Fractional Brownian Motions: a Reconsideration," Discussion Papers 0816, Exeter University, Department of Economics.
  3. Søren Johansen, 2010. "An Extension of Cointegration to Fractional Autoregressive Processes," Discussion Papers 10-28, University of Copenhagen. 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. Morten Ørregaard Nielsen, 2009. "Nonparametric Cointegration Analysis of Fractional Systems With Unknown Integration Orders," CREATES Research Papers 2009-02, School of Economics and Management, University of Aarhus.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  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. Giuseppe Cavaliere & Morten Ørregaard Nielsen & A.M. Robert Taylor, 2013. "Bootstrap Score Tests for Fractional Integration in Heteroskedastic ARFIMA Models, with an Application to Price Dynamics in Commodity Spot and Futures Markets," Working Papers 1309, Queen's University, Department of Economics.

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:kud:kuiedp:0727. 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: (Thomas Hoffmann).

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.