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Nonlinear Functions and Convergence to Brownian Motion: Beyond the Continuous Mapping Theorem

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Abstract

Weak convergence results for sample averages of nonlinear functions of (discrete-time) stochastic processes satisfying a functional central limit theorem (e.g., integrated processes) are given. These results substantially extend recent work by Park and Phillips (1999) and de Jong (2001), in that a much wider class of functions is covered. For example, some of the results hold for the class of all locally integrable functions, thus avoiding any of the various regularity conditions imposed on the functions in Park and Phillips (1999) or de Jong (2001).

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File URL: http://homepage.univie.ac.at/Papers.Econ/RePEc/vie/viennp/vie0203.pdf
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Bibliographic Info

Paper provided by University of Vienna, Department of Economics in its series Vienna Economics Papers with number 0203.

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Date of creation: Nov 2001
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Handle: RePEc:vie:viennp:0203

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Web page: http://www.univie.ac.at/vwl

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Cited by:
  1. de Jong, Robert M., 2003. "Logarithmic spurious regressions," Economics Letters, Elsevier, vol. 81(1), pages 13-21, October.

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