The impact of stationarity assessment on studies of volatility and value-at-risk

  • Authors:

  • J. Lekow

  • Affiliations:

  • Institute of Mathematics, Technical University of Wrocaw Wrocaw, Poland and Centro de Investigacion en Matematicas CIMAT Guanajuato, Mexico

  • Venue:
  • Mathematical and Computer Modelling: An International Journal
  • Year:
  • 2001

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Abstract

Recent research on volatility of asset returns demonstrates that model innovations frequently show unconditional heteroscedasticity. On the other hand, ARMA-GARCH models incorporate the heteroscedasticity only in the conditional distribution of the innovations, assuming the unconditional distributions to be stationary (see, e.g., [1,2]). Given the observed unconditional heteroscedasticity of the return innovations [3], there is a need to overcome this shortcoming of existing models. The purpose of this paper is to introduce a test of stationarity of the innovations and show its impact in the analysis of volatility and value at risk. The methodological results are accompanied with examples and simulations.