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Nonlinear Persistence and Copersistence


  • 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.

Suggested Citation

  • Christian Gourieroux & Joann Jasiak, 1999. "Nonlinear Persistence and Copersistence," Working Papers 2000_1, York University, Department of Economics.
  • Handle: RePEc:yca:wpaper:2000_1

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    References listed on IDEAS

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    More about this item


    Nonlinear Autocorrelogram; Canonical Analysis; Persistence; Chaos; Unit Root; Cointegration;

    JEL classification:

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


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