IDEAS home Printed from https://ideas.repec.org/a/cup/etheor/v16y2000i06p878-904_16.html
   My bibliography  Save this article

Mixed Normality And Ancillarity In I(2) Systems

Author

Listed:
  • Boswijk, H. Peter

Abstract

This paper studies asymptotic likelihood inference on cointegration parameters in systems integrated of order two. We start with so-called triangular systems and then extend the analysis to vector autoregressions. We show that even when all unit root restrictions have been imposed, the asymptotic observed information is not (locally) ancillary, which implies that the log-likelihood ratio is not locally asymptotically mixed normal. The results are applied to inference on polynomial cointegration. Some similarities and differences with I(1) systems are also discussed.

Suggested Citation

  • Boswijk, H. Peter, 2000. "Mixed Normality And Ancillarity In I(2) Systems," Econometric Theory, Cambridge University Press, vol. 16(6), pages 878-904, December.
    • Handle: RePEc:cup:etheor:v:16:y:2000:i:06:p:878-904_16
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S0266466600166046/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jurgen A. Doornik & Rocco Mosconi & Paolo Paruolo, 2017. "Formula I(1) and I(2): Race Tracks for Likelihood Maximization Algorithms of I(1) and I(2) Cointegrated VAR Models," Econometrics, MDPI, vol. 5(4), pages 1-30, November.
    2. Paruolo, Paolo, 2006. "Common trends and cycles in I(2) VAR systems," Journal of Econometrics, Elsevier, vol. 132(1), pages 143-168, May.
    3. Mosconi, Rocco & Paruolo, Paolo, 2017. "Identification conditions in simultaneous systems of cointegrating equations with integrated variables of higher order," Journal of Econometrics, Elsevier, vol. 198(2), pages 271-276.
    4. H. Peter Boswijk & Jurgen A. Doornik, 2004. "Identifying, estimating and testing restricted cointegrated systems: An overview," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(4), pages 440-465, November.
    5. Kurita, Takamitsu, 2020. "Likelihood-based tests for parameter constancy in I(2) CVAR models with an application to fixed-term deposit data," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    6. Kristensen, Dennis & Rahbek, Anders, 2010. "Likelihood-based inference for cointegration with nonlinear error-correction," Journal of Econometrics, Elsevier, vol. 158(1), pages 78-94, September.
    7. Johansen, Soren, 2006. "Statistical analysis of hypotheses on the cointegrating relations in the I(2) model," Journal of Econometrics, Elsevier, vol. 132(1), pages 81-115, May.
    8. Takamitsu Kurita, 2009. "A note on testing parameter constancy in cointegrated vector autoregression: the case of near I(2) processes," Economics Bulletin, AccessEcon, vol. 29(2), pages 575-587.
    9. Søren Johansen & Katarina Juselius & Roman Frydman & Michael Goldberg, 2007. "Testing Hypotheses in an I(2) Model with Applications to the Persistent Long Swings in the Dmk/$ Rate," Discussion Papers 07-34, University of Copenhagen. Department of Economics.
    10. Kheifets, Igor L. & Phillips, Peter C.B., 2023. "Fully modified least squares cointegrating parameter estimation in multicointegrated systems," Journal of Econometrics, Elsevier, vol. 232(2), pages 300-319.
    11. Phillips, Peter C.B. & Kheifets, Igor L., 2024. "High-dimensional IV cointegration estimation and inference," Journal of Econometrics, Elsevier, vol. 238(2).
    12. Helmut Lütkepohl, 2013. "Vector autoregressive models," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 6, pages 139-164, Edward Elgar Publishing.
    13. Johansen, Søren & Juselius, Katarina & Frydman, Roman & Goldberg, Michael, 2010. "Testing hypotheses in an I(2) model with piecewise linear trends. An analysis of the persistent long swings in the Dmk/$ rate," Journal of Econometrics, Elsevier, vol. 158(1), pages 117-129, September.
    14. Helmut Luetkepohl, 2007. "Econometric Analysis with Vector Autoregressive Models," Economics Working Papers ECO2007/11, European University Institute.
    15. Mosconi, Rocco & Paruolo, Paolo, 2014. "Rank and order conditions for identification in simultaneous system of cointegrating equations with integrated variables of order two," MPRA Paper 53589, University Library of Munich, Germany.
    16. H. Peter Boswijk & Paolo Paruolo, 2017. "Likelihood Ratio Tests of Restrictions on Common Trends Loading Matrices in I(2) VAR Systems," Econometrics, MDPI, vol. 5(3), pages 1-17, June.

    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:16:y:2000:i:06:p:878-904_16. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.