Asymptotics for functionals of self-normalized residuals of discretely observed stochastic processes

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The purpose of this paper is to derive the stochastic expansion of self-normalized-residual functionals stemming from a class of diffusion type processes observed at high frequency, where total observing period may or may not tend to infinity. The result enables us to construct some explicit statistics for goodness of fit tests, consistent against "presence of a jump component" and "diffusion-coefficient misspecification"; then, the acceptance of the null hypothesis may serve as a collateral evidence for using the correctly specified diffusion type model. Especially, our asymptotic result clarifies how to remove the bias caused by plugging in a diffusion-coefficient estimator.

Original languageEnglish
Pages (from-to)2752-2778
Number of pages27
JournalStochastic Processes and their Applications
Issue number7
Publication statusPublished - Jan 1 2013


All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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