IDEAS home Printed from https://ideas.repec.org/p/mtl/montde/9817.html
   My bibliography  Save this paper

The FCLT with Dependent Errors: an Helicopter Tour of the Quality of the Approximation

Author

Listed:
  • PERRON, Pierre
  • MALLET, Sylvie

Abstract

This note investigates the adequacy of the finite-sample approximation provided by the Functional Central Limit Theorem (FCLT) when the errors are allowed to be dependent. We compare the distribution of the scaled partial sums of some data with the distribution of the Wiener process to which it converges. Our setup is purposely very simple in that it considers data generated from an ARMA(1,1) process. Yet, this is sufficient to bring out interesting conclusions about the particular elements which cause the approximations to be inadequate in even quite large sample sizes.

Suggested Citation

  • PERRON, Pierre & MALLET, Sylvie, 1998. "The FCLT with Dependent Errors: an Helicopter Tour of the Quality of the Approximation," Cahiers de recherche 9817, Universite de Montreal, Departement de sciences economiques.
    • Handle: RePEc:mtl:montde:9817
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/1866/466
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Perron, Pierre, 1996. "The adequacy of asymptotic approximations in the near-integrated autoregressive model with dependent errors," Journal of Econometrics, Elsevier, vol. 70(2), pages 317-350, February.
    2. Pierre Perron & Serena Ng, 1996. "Useful Modifications to some Unit Root Tests with Dependent Errors and their Local Asymptotic Properties," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(3), pages 435-463.
    3. Nabeya, Seiji & Perron, Pierre, 1994. "Local asymptotic distribution related to the AR(1) model with dependent errors," Journal of Econometrics, Elsevier, vol. 62(2), pages 229-264, June.
    Full references (including those not matched with items on IDEAS)

    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. Serena Ng & Pierre Perron, 2002. "PPP May not Hold Afterall: A Further Investigation," Annals of Economics and Finance, Society for AEF, vol. 3(1), pages 43-64, May.
    2. Ng, Serena & Perron, Pierre, 1997. "Estimation and inference in nearly unbalanced nearly cointegrated systems," Journal of Econometrics, Elsevier, vol. 79(1), pages 53-81, July.
    3. Perron, Pierre & Mallet, Sylvie, 2000. "A look at the quality of the approximation of the functional central limit theorem," Economics Letters, Elsevier, vol. 68(3), pages 225-234, September.
    4. Ai Deng, 2014. "Understanding Spurious Regression in Financial Economics," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 122-150.
    5. Niels Haldrup & Peter Lildholdt, 2002. "On the Robustness of Unit Root Tests in the Presence of Double Unit Roots," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(2), pages 155-171, March.
    6. Margolis, D..N., 1995. "Firm Heterogeneity and Worker Self-Selection Bias Estimated Returns to Seniority," Cahiers de recherche 9502, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    7. Nunzio Cappuccio & Diego Lubian, 2003. "Asymptotic null distributions of stationarity and nonstationarity," Working Papers 08/2003, University of Verona, Department of Economics.
    8. Ai Deng Author-X-Name-First: Ai, 2006. "Local Power of Andrews and Ploberger Tests Against Nearly Integrated, Nearly White Noise Process," Boston University - Department of Economics - Working Papers Series WP2006-027, Boston University - Department of Economics.
    9. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
    10. Tomás Del Barrio Castro & Paulo M. M. Rodrigues & A. M. Robert Taylor, 2015. "On the Behaviour of Phillips–Perron Tests in the Presence of Persistent Cycles," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 77(4), pages 495-511, August.
    11. Qu, Zhongjun & Perron, Pierre, 2007. "A Modified Information Criterion For Cointegration Tests Based On A Var Approximation," Econometric Theory, Cambridge University Press, vol. 23(4), pages 638-685, August.
    12. Zou, Nan & Politis, Dimitris N., 2019. "Linear process bootstrap unit root test," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 74-80.
    13. Niels Haldrup & Peter Lildholdt, 2005. "Local power functions of tests for double unit roots," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(2), pages 159-179, May.
    14. Marco Morales, 2014. "Cointegration testing under structural change: reducing size distortions and improving power of residual based tests," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(2), pages 265-282, June.
    15. Deng, Ai, 2010. "Local power of consistent tests for serial correlation against the nearly integrated, nearly white noise process," Economics Letters, Elsevier, vol. 107(1), pages 22-25, April.
    16. Vassilis Monastiriotis & Cigdem Borke Tunali, 2020. "The Sustainability of External Imbalances in the European Periphery," Open Economies Review, Springer, vol. 31(2), pages 273-294, April.
    17. Óscar Bajo Rubio & Carmen Díaz Roldán & Vicente Esteve, 2004. "Is the Fisher Effect Nonlinear? Some Evidence for Spain, 1963-2002," Economic Working Papers at Centro de Estudios Andaluces E2004/05, Centro de Estudios Andaluces.
    18. Bajo-Rubio, Oscar & Díaz-Roldán, Carmen & Esteve, Vicente, 2014. "Deficit sustainability, and monetary versus fiscal dominance: The case of Spain, 1850–2000," Journal of Policy Modeling, Elsevier, vol. 36(5), pages 924-937.
    19. Vicente Esteve & Manuel Navarro-Ibáñez & María A. Prats, 2013. "The present value model of US stock prices revisited: long-run evidence with structural breaks, 1871-2010," Working Papers 04/13, Instituto Universitario de Análisis Económico y Social.
    20. Elliott, Graham, 2020. "Testing for a trend with persistent errors," Journal of Econometrics, Elsevier, vol. 219(2), pages 314-328.

    More about this item

    Keywords

    Wiener ocess; Brownian bridge; distribution function; serial correlation; asymotic aroximation;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

    Statistics

    Access and download statistics

    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:mtl:montde:9817. 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: Sharon BREWER (email available below). General contact details of provider: https://edirc.repec.org/data/demtlca.html .

    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.