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Carmichael's Arctan Trend: Precursor of Smooth Transition Functions

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  • Terence Mills

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

  • Kerry Patterson

    ()
    (Department of Economics, University of Reading)

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    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.

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    Bibliographic Info

    Paper provided by Henley Business School, Reading University in its series Economics & Management Discussion Papers with number em-dp2013-06.

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    Length: 14 pages
    Date of creation: 15 Oct 2013
    Date of revision:
    Handle: RePEc:rdg:emxxdp:em-dp2013-06

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    1. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    2. Donald W.K. Andrews, 1990. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Cowles Foundation Discussion Papers 943, Cowles Foundation for Research in Economics, Yale University.
    3. 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 S119-36, Suppl. De.
    4. 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.
    5. 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.
    6. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    7. David Harvey & Terence Mills, 2002. "Unit roots and double smooth transitions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(5), pages 675-683.
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