NONLINEAR FUNCTIONS AND CONVERGENCE TO BROWNIAN MOTION: BEYOND THE CONTINUOUS MAPPING THEOREM

Benedikt M. P tscher

Econometric Theory, 2004, vol. 20, issue 01, pages 1-22

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, Econometric Theory 15, 269 298) and de Jong (2002, working paper), 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 (2002).

Date: 2004
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