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

Hiroki Masuda

    Research output: Contribution to journalArticlepeer-review

    6 Citations (Scopus)

    Abstract

    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
    Volume123
    Issue number7
    DOIs
    Publication statusPublished - 2013

    All Science Journal Classification (ASJC) codes

    • Statistics and Probability
    • Modelling and Simulation
    • Applied Mathematics

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