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Nonlinear Persistence and Copersistence

Listed author(s):
  • Christian Gourieroux

    ()

    (CREST and CEPREMAP)

  • Joann Jasiak

    ()

    (York University, Canada)

In a nonlinear framework, temporal dependence of time series is sensitive to transformations. The aim of this paper is to examine in detail the relationships between various forms of persistence and nonlinear transformations of stationary and nonstationary processes. We introduce the concept of persistence space and use it to define the degrees of persistence of univariate or multivariate processes. For illustration, we examine and compare the persistence structure of a fractionally integrated process and a beta mixture of AR(1) processes. The study of multivariate processes is focused on nonlinear comovements between the components, called the copersistence directions, or cointegration directions in the nonstationary case. We nd that, in general, there is a multiplicity of such directions, causing an identi cation problem in the analysis of nonlinear cointegration.

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File URL: http://dept.econ.yorku.ca/research/workingPapers/working_papers/coper.pdf
File Function: First version, 1999
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Paper provided by York University, Department of Economics in its series Working Papers with number 2000_1.

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Length: 34 pages
Date of creation: Nov 1999
Handle: RePEc:yca:wpaper:2000_1
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Web page: http://dept.econ.yorku.ca/

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  1. Vahid, F & Engle, Robert F, 1993. "Common Trends and Common Cycles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(4), pages 341-360, Oct.-Dec..
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  12. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
  13. Hansen, Lars Peter & Alexandre Scheinkman, Jose & Touzi, Nizar, 1998. "Spectral methods for identifying scalar diffusions," Journal of Econometrics, Elsevier, vol. 86(1), pages 1-32, June.
  14. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(03), pages 269-298, June.
  15. He, Changli & Teräsvirta, Timo, 1997. "Statistical Properties of the Asymmetric Power ARCH Process," SSE/EFI Working Paper Series in Economics and Finance 199, Stockholm School of Economics, revised 30 Sep 1997.
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