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

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  • Christopeit, Norbert

Abstract

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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  • Christopeit, Norbert, 2009. "Weak Convergence Of Nonlinear Transformations Of Integrated Processes: The Multivariate Case," Econometric Theory, Cambridge University Press, vol. 25(5), pages 1180-1207, October.
    • Handle: RePEc:cup:etheor:v:25:y:2009:i:05:p:1180-1207_09
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    Cited by:

    1. Pötscher, Benedikt M., 2013. "On The Order Of Magnitude Of Sums Of Negative Powers Of Integrated Processes," Econometric Theory, Cambridge University Press, vol. 29(3), pages 642-658, June.
    2. Zhishui Hu & Ioannis Kasparis & Qiying Wang, 2020. "Locally trimmed least squares: conventional inference in possibly nonstationary models," Papers 2006.12595, arXiv.org.

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