IDEAS home Printed from https://ideas.repec.org/p/rdg/emxxdp/em-dp2013-06.html
   My bibliography  Save this paper

Carmichael's Arctan Trend: Precursor of Smooth Transition Functions

Author

Listed:
  • Terence Mills

    () (School of Business and Economics, Loughborough University)

  • Kerry Patterson

    () (Department of Economics, University of Reading)

Abstract

In an almost unreferenced article Carmichael (1928), writing of the period around the First World War, noted that “During the past twelve years many economic series have undergone what appears to be a permanent change in level.” These are prescient words that are widely applicable today. Carmichael noted that the then standard method of linear detrending was inappropriate in the presence of what we would now call structural breaks; as a result he proposed a method that would not only model a nonlinear trend, but would be suitable for situations where the transition from one regime to another was smooth in the sense that we now associate with LSTAR transition functions. Moreover, in an even greater understanding of the underlying processes, he extended the possibility of transition to a double transition, a clear but unacknowledged precursor of recent work in that area. This study establishes the precedence of Carmichael’s work, re-examines his methods and solves the problems that he thought would hinder the then wider applications of his approach. Carmichael shows considerable skill in assessing the complex practical problems of determining the switch points and strength of adjustment of the proposed transition functions.

Suggested Citation

  • Terence Mills & Kerry Patterson, 2013. "Carmichael's Arctan Trend: Precursor of Smooth Transition Functions," Economics & Management Discussion Papers em-dp2013-06, Henley Business School, Reading University.
  • Handle: RePEc:rdg:emxxdp:em-dp2013-06
    as

    Download full text from publisher

    File URL: http://www.reading.ac.uk/web/FILES/economics/emdp2013103.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Terasvirta, T & Anderson, H M, 1992. "Characterizing Nonlinearities in Business Cycles Using Smooth Transition Autoregressive Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages 119-136, Suppl. De.
    2. David Harvey & Terence Mills, 2002. "Unit roots and double smooth transitions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(5), pages 675-683.
    3. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    4. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    5. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    6. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    7. Aldrich, J., 1995. "Correlations genuine and spurious in Pearson and Yule," Discussion Paper Series In Economics And Econometrics 9502, Economics Division, School of Social Sciences, University of Southampton.
    8. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    n.a.;

    JEL classification:

    • N - Economic History
    • A - General Economics and Teaching

    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:rdg:emxxdp:em-dp2013-06. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Marie Pearson). General contact details of provider: http://edirc.repec.org/data/bsrdguk.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.