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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).

Suggested Citation

  • Benedikt M. Pötscher, 2001. "Nonlinear Functions and Convergence to Brownian Motion: Beyond the Continuous Mapping Theorem," Vienna Economics Papers 0203, University of Vienna, Department of Economics.
  • Handle: RePEc:vie:viennp:0203
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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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    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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