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Nonlinear persistence and copersistence

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  • Gourieroux, Christian
  • Josiak, Joann

Abstract

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 find that, in general, there is multiplicity of such directions, causing an identification problem in the analysis of nonlinear cointegration.

Suggested Citation

  • Gourieroux, Christian & Josiak, Joann, 1999. "Nonlinear persistence and copersistence," CEPREMAP Working Papers (Couverture Orange) 9920, CEPREMAP.
    • Handle: RePEc:cpm:cepmap:9920
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    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. Non-linear Functions of Non-Stationary Data Can be Stationary
      by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2013-02-27 03:17:00

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    Cited by:

    1. Dittmann, Ingolf & Granger, Clive W. J., 2002. "Properties of nonlinear transformations of fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 110(2), pages 113-133, October.
    2. Darolles, Serge & Florens, Jean-Pierre & Gourieroux, Christian, 2004. "Kernel-based nonlinear canonical analysis and time reversibility," Journal of Econometrics, Elsevier, vol. 119(2), pages 323-353, April.

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    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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