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Weak Convergence Of Nonlinear Transformations Of Integrated Processes: The Multivariate Case

  • Christopeit, Norbert
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    We consider weak convergence of sample averages of nonlinearly transformed stochastic triangular arrays satisfying a functional invariance principle. A fundamental paradigm for such processes is constituted by integrated processes. The results obtained are extensions of recent work in the literature to the multivariate and non-Gaussian case. As admissible nonlinear transformation, a new class of functionals (so-called locally p -integrable functions) is introduced that adapts the concept of locally integrable functions in Pötscher (2004, Econometric Theory 20, 1–22) to the multidimensional setting.

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    File URL: http://journals.cambridge.org/abstract_S0266466608090476
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    Article provided by Cambridge University Press in its journal Econometric Theory.

    Volume (Year): 25 (2009)
    Issue (Month): 05 (October)
    Pages: 1180-1207

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    Handle: RePEc:cup:etheor:v:25:y:2009:i:05:p:1180-1207_09
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