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Characteristic function approach to the sum of stochastic variables

Author

Listed:
  • Figueiredo, Annibal
  • Gleria, Iram
  • Matsushita, Raul
  • Da Silva, Sergio

Abstract

This paper puts forward a technique based on the characteristic function to tackle the problem of the sum of stochastic variables. We consider independent processes whose reduced variables are identically distributed, including those that violate the conditions for the central limit theorem to hold. We also consider processes that are correlated and analyze the role of nonlinear autocorrelations in their convergence to a Gaussian. We demonstrate that nonidentity in independent processes is related to autocorrelations in nonindependent processes. We exemplify our approach with data from foreign exchange rates.

Suggested Citation

  • Figueiredo, Annibal & Gleria, Iram & Matsushita, Raul & Da Silva, Sergio, 2006. "Characteristic function approach to the sum of stochastic variables," MPRA Paper 1984, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:1984
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    File URL: https://mpra.ub.uni-muenchen.de/1984/1/MPRA_paper_1984.pdf
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    References listed on IDEAS

    as
    1. Figueiredo, Annibal & Gleria, Iram & Matsushita, Raul & Da Silva, Sergio, 2005. "Financial volatility and independent and identically distributed variables," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 346(3), pages 484-498.
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      Keywords

      econophysics; central limit theorem; characteristic function; reduced variables; autocorrelation;
      All these keywords.

      JEL classification:

      • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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