IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v62y2003i2p163-173.html
   My bibliography  Save this article

A bootstrap approximation to a unit root test statistic for heavy-tailed observations

Author

Listed:
  • Horváth, Lajos
  • Kokoszka, Piotr

Abstract

In the context of the AR(1) model with innovations in the domain of attraction of an [alpha]-stable law, we develop a residual bootstrap approximation to the distribution of a least-squares estimator of the autoregressive parameter when this parameter is equal to unity. Our procedure requires drawing bootstrap samples of size m [infinity] and m/n-->0. An analogous result is established for the partial sum process of the bootstrap noise sequence.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:62:y:2003:i:2:p:163-173
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(03)00007-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Peter C. B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-470, December.
    2. Knight, Keith, 1991. "Limit Theory for M-Estimates in an Integrated Infinite Variance," Econometric Theory, Cambridge University Press, vol. 7(2), pages 200-212, June.
    3. 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.
    4. 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.
    5. 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.
    6. Peter C. B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-470, December.
    7. Heimann, Günter & Kreiss, Jens-Peter, 1996. "Bootstrapping general first order autoregression," Statistics & Probability Letters, Elsevier, vol. 30(1), pages 87-98, 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


    Cited by:

    1. Jin, Hao & Zhang, Jinsuo, 2011. "Modified tests for variance changes in autoregressive regression," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(6), pages 1099-1109.
    2. Jin, Hao & Tian, Zheng & Qin, Ruibing, 2009. "Bootstrap tests for structural change with infinite variance observations," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 1985-1995, October.
    3. Qin, Ruibing & Tian, Zheng & Jin, Hao & Zhang, Xiaowei, 2010. "Strong convergence rate of robust estimator of change point," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2026-2032.
    4. 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.
    5. 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.
    6. 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.
    7. Hao Jin & Si Zhang & Jinsuo Zhang, 2017. "Spurious regression due to neglected of non-stationary volatility," Computational Statistics, Springer, vol. 32(3), pages 1065-1081, September.
    8. 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.
    9. Serttas, Fatma Ozgu, 2010. "Essays on infinite-variance stable errors and robust estimation procedures," ISU General Staff Papers 201001010800002742, Iowa State University, Department of Economics.
    10. Christis Katsouris, 2023. "Bootstrapping Nonstationary Autoregressive Processes with Predictive Regression Models," Papers 2307.14463, arXiv.org.

    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. 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.
    2. Lima Luiz Renato & Xiao Zhijie, 2010. "Testing Unit Root Based on Partially Adaptive Estimation," Journal of Time Series Econometrics, De Gruyter, vol. 2(1), pages 1-34, June.
    3. Xiao, Zhijie, 2004. "Estimating average economic growth in time series data with persistency," Journal of Macroeconomics, Elsevier, vol. 26(4), pages 699-724, December.
    4. Muriel, Nelson & González-Farías, Graciela, 2018. "Testing the null of difference stationarity against the alternative of a stochastic unit root: A new test based on multivariate STUR," Econometrics and Statistics, Elsevier, vol. 7(C), pages 46-62.
    5. Brendan K. Beare, 2018. "Unit Root Testing with Unstable Volatility," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 816-835, November.
    6. Ventosa-Santaularària, Daniel & Gómez, Manuel, 2006. "Inflation and Breaks: the validity of the Dickey-Fuller test," MPRA Paper 58773, University Library of Munich, Germany.
    7. Christoph Rothe & Philipp Sibbertsen, 2006. "Phillips-Perron-type unit root tests in the nonlinear ESTAR framework," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 90(3), pages 439-456, September.
    8. 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.
    9. Christophe Kamps, 2006. "New Estimates of Government Net Capital Stocks for 22 OECD Countries, 1960-2001," IMF Staff Papers, Palgrave Macmillan, vol. 53(1), pages 1-6.
    10. Hyungsik R. Moon & Peter C.B. Phillips, 1999. "Maximum Likelihood Estimation in Panels with Incidental Trends," Cowles Foundation Discussion Papers 1246, Cowles Foundation for Research in Economics, Yale University.
    11. Werner Ploberger & Peter C.B. Phillips, 1998. "Rissanen's Theorem and Econometric Time Series," Cowles Foundation Discussion Papers 1197, Cowles Foundation for Research in Economics, Yale University.
    12. Franco Bevilacqua & Adriaan van Zon, 2004. "Random walks and non-linear paths in macroeconomic time series: some evidence and implications," Chapters, in: John Foster & Werner Hölzl (ed.), Applied Evolutionary Economics and Complex Systems, chapter 3, Edward Elgar Publishing.
    13. Geweke, J. & Joel Horowitz & Pesaran, M.H., 2006. "Econometrics: A Bird’s Eye View," Cambridge Working Papers in Economics 0655, Faculty of Economics, University of Cambridge.
    14. Nielsen, Morten, 2008. "A Powerful Tuning Parameter Free Test of the Autoregressive Unit Root Hypothesis," Working Papers 08-05, Cornell University, Center for Analytic Economics.
    15. Michael Jansson & Morten Ørregaard Nielsen, 2012. "Nearly Efficient Likelihood Ratio Tests of the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 80(5), pages 2321-2332, September.
    16. Nielsen, Morten Ørregaard, 2009. "A Powerful Test Of The Autoregressive Unit Root Hypothesis Based On A Tuning Parameter Free Statistic," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1515-1544, December.
    17. Charles Nelson & Jeremy Piger & Eric Zivot, 1999. "Unit Root Tests in the Presence of Markov Regime-Switching," Discussion Papers in Economics at the University of Washington 0040, Department of Economics at the University of Washington.
    18. Alain Kabundi & Elsabé Loots, 2010. "Patterns Of Co‐Movement Between South Africa And Germany: Evidence From The Period 1985 To 2006," South African Journal of Economics, Economic Society of South Africa, vol. 78(4), pages 383-399, December.
    19. Rodrigues, Paulo M. M. & Taylor, A. M. Robert, 2004. "Alternative estimators and unit root tests for seasonal autoregressive processes," Journal of Econometrics, Elsevier, vol. 120(1), pages 35-73, May.
    20. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2013. "Unit roots, non-linearities and structural breaks," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 4, pages 61-94, Edward Elgar Publishing.

    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:eee:stapro:v:62:y:2003:i:2:p:163-173. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.