IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v6y2004i1d10.1023_bmcap.0000012416.28866.c5.html
   My bibliography  Save this article

Subsampling Unit Root Tests for Heavy-Tailed Observations

Author

Listed:
  • Agnieszka Jach

    (Utah State University)

  • Piotr Kokoszka

    (Utah State University)

Abstract

It is shown that the subsampling methodology can be used to develop unit root tests when the noise sequence is heavy-tailed with infinite variance. Using least-squares residuals, we construct processes which approximately satisfy the null hypothesis and then, using subsampling, we approximate the null distribution of test statistics. We establish the asymptotic validity of this method and demonstrate its applicability in finite samples by means of a simulation study and a data example.

Suggested Citation

  • Agnieszka Jach & Piotr Kokoszka, 2004. "Subsampling Unit Root Tests for Heavy-Tailed Observations," Methodology and Computing in Applied Probability, Springer, vol. 6(1), pages 73-97, March.
    • Handle: RePEc:spr:metcap:v:6:y:2004:i:1:d:10.1023_b:mcap.0000012416.28866.c5
    DOI: 10.1023/B:MCAP.0000012416.28866.c5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/B:MCAP.0000012416.28866.c5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/B:MCAP.0000012416.28866.c5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Richard B. Olsen & Ulrich A. Müller & Michel M. Dacorogna & Olivier V. Pictet & Rakhal R. Davé & Dominique M. Guillaume, 1997. "From the bird's eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets (*)," Finance and Stochastics, Springer, vol. 1(2), pages 95-129.
    2. Ling, Shiqing & Li, W.K., 2003. "Asymptotic Inference For Unit Root Processes With Garch(1,1) Errors," Econometric Theory, Cambridge University Press, vol. 19(4), pages 541-564, August.
    3. 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 1057-1072, June.
    4. Swensen, Anders Rygh, 2003. "A Note On The Power Of Bootstrap Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 19(1), pages 32-48, February.
    5. Wang, Qiying & Lin, Yan-Xia & Gulati, Chandra M., 2003. "Asymptotics For General Fractionally Integrated Processes With Applications To Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 19(1), pages 143-164, February.
    6. Horváth, Lajos & Kokoszka, Piotr, 2003. "A bootstrap approximation to a unit root test statistic for heavy-tailed observations," Statistics & Probability Letters, Elsevier, vol. 62(2), pages 163-173, April.
    7. Efstathios Paparoditis & Dimitris N. Politis, 2003. "Residual-Based Block Bootstrap for Unit Root Testing," Econometrica, Econometric Society, vol. 71(3), pages 813-855, May.
    8. Chan, Ngai Hang & Tran, Lanh Tat, 1989. "On the First-Order Autoregressive Process with Infinite Variance," Econometric Theory, Cambridge University Press, vol. 5(3), pages 354-362, December.
    9. Heimann, Günter & Kreiss, Jens-Peter, 1996. "Bootstrapping general first order autoregression," Statistics & Probability Letters, Elsevier, vol. 30(1), pages 87-98, September.
    10. Berkes, István & Horváth, Lajos & Kokoszka, Piotr, 2003. "Estimation Of The Maximal Moment Exponent Of A Garch(1,1) Sequence," Econometric Theory, Cambridge University Press, vol. 19(4), pages 565-586, August.
    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


    Cited by:

    1. Arvanitis, Stelios, 2017. "A note on the limit theory of a Dickey–Fuller unit root test with heavy tailed innovations," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 198-204.
    2. Matteo Barigozzi & Giuseppe Cavaliere & Lorenzo Trapani, 2021. "Inference in heavy-tailed non-stationary multivariate time series," Papers 2107.13894, arXiv.org.
    3. Kirman, Alan & Teyssiere, Gilles, 2005. "Testing for bubbles and change-points," Journal of Economic Dynamics and Control, Elsevier, vol. 29(4), pages 765-799, April.
    4. D. M. Mahinda Samarakoon & Keith Knight, 2009. "A Note on Unit Root Tests with Infinite Variance Noise," Econometric Reviews, Taylor & Francis Journals, vol. 28(4), pages 314-334.
    5. Jin, Hao & Zhang, Jinsuo, 2010. "Subsampling tests for variance changes in the presence of autoregressive parameter shifts," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2255-2265, November.
    6. Jin, Hao & Tian, Zheng & Qin, Ruibing, 2009. "Subsampling tests for the mean change point with heavy-tailed innovations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2157-2166.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Horváth, Lajos & Kokoszka, Piotr, 2003. "A bootstrap approximation to a unit root test statistic for heavy-tailed observations," Statistics & Probability Letters, Elsevier, vol. 62(2), pages 163-173, April.
    2. Franz C. Palm & Stephan Smeekes & Jean‐Pierre Urbain, 2008. "Bootstrap Unit‐Root Tests: Comparison and Extensions," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(2), pages 371-401, March.
    3. Stephan Smeekes, 2013. "Detrending Bootstrap Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, vol. 32(8), pages 869-891, November.
    4. Kirman, Alan & Teyssiere, Gilles, 2005. "Testing for bubbles and change-points," Journal of Economic Dynamics and Control, Elsevier, vol. 29(4), pages 765-799, April.
    5. Nikolaos Kourogenis & Nikitas Pittis, 2008. "Testing for a unit root under errors with just barely infinite variance," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(6), pages 1066-1087, November.
    6. C. Lawrenz & F. Westerhoff, 2003. "Modeling Exchange Rate Behavior with a Genetic Algorithm," Computational Economics, Springer;Society for Computational Economics, vol. 21(3), pages 209-229, June.
    7. C. Jentsch & J.-P. Kreiss & P. Mantalos & E. Paparoditis, 2012. "Hybrid bootstrap aided unit root testing," Computational Statistics, Springer, vol. 27(4), pages 779-797, December.
    8. Michael Jansson, 2008. "Semiparametric Power Envelopes for Tests of the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 76(5), pages 1103-1142, September.
    9. Parker, Cameron & Paparoditis, Efstathios & Politis, Dimitris N., 2006. "Unit root testing via the stationary bootstrap," Journal of Econometrics, Elsevier, vol. 133(2), pages 601-638, August.
    10. Nikolay Gospodinov & Ye Tao, 2011. "Bootstrap Unit Root Tests in Models with GARCH(1,1) Errors," Econometric Reviews, Taylor & Francis Journals, vol. 30(4), pages 379-405, August.
    11. Chen, Zhanshou & Jin, Zi & Tian, Zheng & Qi, Peiyan, 2012. "Bootstrap testing multiple changes in persistence for a heavy-tailed sequence," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2303-2316.
    12. Paulo M.M. Rodrigues & Antonio Rubia, 2004. "On The Small Sample Properties Of Dickey Fuller And Maximum Likelihood Unit Root Tests On Discrete-Sampled Short-Term Interest Rates," Working Papers. Serie AD 2004-11, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    13. Atsushi Inoue & Lutz Kilian, 2002. "Bootstrapping Autoregressive Processes with Possible Unit Roots," Econometrica, Econometric Society, vol. 70(1), pages 377-391, January.
    14. Gaowen Wang, 2017. "Modified Unit Root Tests with Nuisance Parameter Free Asymptotic Distributions," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 519-538, June.
    15. Sarwar, Suleman & Tiwari, Aviral Kumar & Tingqiu, Cao, 2020. "Analyzing volatility spillovers between oil market and Asian stock markets," Resources Policy, Elsevier, vol. 66(C).
    16. van Giersbergen, Noud P. A., 2003. "A note on bootstrapping unit root tests in the presence of a non-zero drift," Economics Letters, Elsevier, vol. 78(2), pages 259-265, February.
    17. Li, Yushu & Shukur, Ghazi, 2009. "Wavelet Improvement of the Over-rejection of Unit root test under GARCH errors," CAFO Working Papers 2009:7, Linnaeus University, Centre for Labour Market Policy Research (CAFO), School of Business and Economics.
    18. Abadir, Karim M. & Distaso, Walter, 2007. "Testing joint hypotheses when one of the alternatives is one-sided," Journal of Econometrics, Elsevier, vol. 140(2), pages 695-718, October.
    19. Sebastian Kripfganz & Daniel C. Schneider, 2020. "Response Surface Regressions for Critical Value Bounds and Approximate p‐values in Equilibrium Correction Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(6), pages 1456-1481, December.
    20. Wang, Gaowen, 2006. "A note on unit root tests with heavy-tailed GARCH errors," Statistics & Probability Letters, Elsevier, vol. 76(10), pages 1075-1079, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:6:y:2004:i:1:d:10.1023_b:mcap.0000012416.28866.c5. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.