The increment ratio statistic

  • Authors:

  • Donatas Surgailis;Gilles Teyssière;Marijus Vaičiulis

  • Affiliations:

  • Vilnius Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania;SAMOS, CES, Université Paris 1 Panthéon--Sorbonne Centre Pierre Mendès France, 90, Rue de Tolbiac - 75634 Paris Cedex 13, France and Centre for Finance, Göteborg University, Bo ...;Vilnius Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2008

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Abstract

We introduce a new statistic written as a sum of certain ratios of second-order increments of partial sums process S"n=@?"t"="1^nX"t of observations, which we call the increment ratio (IR) statistic. The IR statistic can be used for testing nonparametric hypotheses for d-integrated (-12~. For Gaussian observations X"t, we obtain a rate of decay of the bias EIR-@L(d) and a central limit theorem (N/m)^1^/^2(IR-EIR)-N(0,@s^2(d)), in the region -12