IDEAS home Printed from https://ideas.repec.org/a/cup/etheor/v29y2013i06p1162-1195_00.html
   My bibliography  Save this article

Exploiting Infinite Variance Through Dummy Variables In Nonstationary Autoregressions

Author

Listed:
  • Cavaliere, Giuseppe
  • Georgiev, Iliyan

Abstract

We consider estimation and testing in finite-order autoregressive models with a (near) unit root and infinite-variance innovations. We study the asymptotic properties of estimators obtained by dummying out “large” innovations, i.e., those exceeding a given threshold. These estimators reflect the common practice of dealing with large residuals by including impulse dummies in the estimated regression. Iterative versions of the dummy-variable estimator are also discussed. We provide conditions on the preliminary parameter estimator and on the threshold that ensure that (i) the dummy-based estimator is consistent at higher rates than the ordinary least squares estimator, (ii) an asymptotically normal test statistic for the unit root hypothesis can be derived, and (iii) order of magnitude gains of local power are obtained.

Suggested Citation

  • Cavaliere, Giuseppe & Georgiev, Iliyan, 2013. "Exploiting Infinite Variance Through Dummy Variables In Nonstationary Autoregressions," Econometric Theory, Cambridge University Press, vol. 29(6), pages 1162-1195, December.
    • Handle: RePEc:cup:etheor:v:29:y:2013:i:06:p:1162-1195_00
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S0266466613000030/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. E ric E ngler & B ent N ielsen, 2009. "The empirical process of autoregressive residuals," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 367-381, July.
    2. Søren Johansen & Bent Nielsen, 2011. "Asymptotic theory for iterated one-step Huber-skip estimators," Discussion Papers 11-29, University of Copenhagen. Department of Economics.
    3. Cavaliere, Giuseppe & Georgiev, Iliyan, 2009. "Robust Inference In Autoregressions With Multiple Outliers," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1625-1661, December.
    4. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    5. 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.
    6. Resnick, Sidney & Greenwood, Priscilla, 1979. "A bivariate stable characterization and domains of attraction," Journal of Multivariate Analysis, Elsevier, vol. 9(2), pages 206-221, June.
    7. Carlos Santos & David Hendry & Soren Johansen, 2008. "Automatic selection of indicators in a fully saturated regression," Computational Statistics, Springer, vol. 23(2), pages 317-335, April.
    8. Hasan, Mohammad N., 2001. "Rank tests of unit root hypothesis with infinite variance errors," Journal of Econometrics, Elsevier, vol. 104(1), pages 49-65, August.
    9. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, January.
    10. Shiqing Ling, 2005. "Self‐weighted least absolute deviation estimation for infinite variance autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 381-393, June.
    11. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    12. Bent Nielsen & Soren Johansen, 2010. "Discussion of The Forward Search: Theory and Data Analysis," Economics Series Working Papers 2010-W02, University of Oxford, Department of Economics.
    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. Søren Johansen & Bent Nielsen, 2011. "Asymptotic theory for iterated one-step Huber-skip estimators," CREATES Research Papers 2011-40, Department of Economics and Business Economics, Aarhus University.
    2. Katleho Makatjane, 2022. "Forecasting Uncertainty Intervals for Return Period of Extreme Daily Electricity Consumption," International Journal of Energy Economics and Policy, Econjournals, vol. 12(4), pages 217-225, July.
    3. Søren Johansen & Bent Nielsen, 2014. "Outlier detection algorithms for least squares time series regression," Economics Papers 2014-W04, Economics Group, Nuffield College, University of Oxford.
    4. Søren Johansen & Bent Nielsen, 2013. "Outlier Detection in Regression Using an Iterated One-Step Approximation to the Huber-Skip Estimator," Econometrics, MDPI, vol. 1(1), pages 1-18, May.
    5. Søren Johansen & Bent Nielsen, 2014. "Optimal hedging with the cointegrated vector autoregressive model," Discussion Papers 14-23, University of Copenhagen. Department of Economics.
    6. Bent Nielsen & Xiyu Jiao, 2016. "Asymptotic Analysis of Iterated 1-step Huber-skip M-estimators with Varying Cut-offs," Economics Papers 2016-W08, Economics Group, Nuffield College, University of Oxford.

    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. repec:bot:quadip:118 is not listed on IDEAS
    2. Neil R. Ericsson, 2021. "Dynamic Econometrics in Action: A Biography of David F. Hendry," International Finance Discussion Papers 1311, Board of Governors of the Federal Reserve System (U.S.).
    3. Porto, Guido G., 2006. "Using survey data to assess the distributional effects of trade policy," Journal of International Economics, Elsevier, vol. 70(1), pages 140-160, September.
    4. Søren Johansen & Bent Nielsen, 2014. "Optimal hedging with the cointegrated vector autoregressive model," Discussion Papers 14-23, University of Copenhagen. Department of Economics.
    5. Marc Hallin & Ramon van den Akker & Bas Werker, 2009. "A class of Simple Semiparametrically Efficient Rank-Based Unit Root Tests," Working Papers ECARES 2009_001, ULB -- Universite Libre de Bruxelles.
    6. Søren Johansen & Bent Nielsen, 2013. "Asymptotic analysis of the Forward Search," Discussion Papers 13-01, University of Copenhagen. Department of Economics.
    7. Søren Johansen & Bent Nielsen, 2014. "Outlier detection algorithms for least squares time series regression," Economics Papers 2014-W04, Economics Group, Nuffield College, University of Oxford.
    8. Brendan K. Beare, 2018. "Unit Root Testing with Unstable Volatility," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 816-835, November.
    9. Hallin, Marc & van den Akker, Ramon & Werker, Bas J.M., 2011. "A class of simple distribution-free rank-based unit root tests," Journal of Econometrics, Elsevier, vol. 163(2), pages 200-214, August.
    10. Dennis Kristensen, 2004. "A Semiparametric Single-Factor Model of the Term Structure," FMG Discussion Papers dp501, Financial Markets Group.
    11. Hasan, Mohammad N., 2001. "Rank tests of unit root hypothesis with infinite variance errors," Journal of Econometrics, Elsevier, vol. 104(1), pages 49-65, August.
    12. Hallin, M. & van den Akker, R. & Werker, B.J.M., 2011. "A Class of Simple Distribution-free Rank-based Unit Root Tests (Revision of DP 2010-72)," Other publications TiSEM 004c9726-ec6a-4884-8238-d, Tilburg University, School of Economics and Management.
    13. Preve, Daniel, 2015. "Linear programming-based estimators in nonnegative autoregression," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 225-234.
    14. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    15. repec:hal:journl:peer-00834424 is not listed on IDEAS
    16. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    17. Erik Hjalmarsson, 2005. "Estimation of average local-to-unity roots in heterogenous panels," International Finance Discussion Papers 852, Board of Governors of the Federal Reserve System (U.S.).
    18. Peter C.B. Phillips & Shu-Ping Shi & Jun Yu, 2011. "Testing for Multiple Bubbles," Working Papers 09-2011, Singapore Management University, School of Economics.
    19. Bierens, H.J. & Broersma, L., 1991. "The relation between unemployment and interest rate : some international evidence," Serie Research Memoranda 0112, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    20. John Barkoulas & Christopher Baum & Mustafa Caglayan, 1999. "Fractional monetary dynamics," Applied Economics, Taylor & Francis Journals, vol. 31(11), pages 1393-1400.
    21. Nicholas Taylor, 1998. "Precious metals and inflation," Applied Financial Economics, Taylor & Francis Journals, vol. 8(2), pages 201-210.
    22. Frankel, Jeffrey A & Schmukler, Sergio L, 2000. "Country Funds and Asymmetric Information," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 5(3), pages 177-195, July.

    More about this item

    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:cup:etheor:v:29:y:2013:i:06:p:1162-1195_00. 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: Kirk Stebbing (email available below). General contact details of provider: https://www.cambridge.org/ect .

    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.