Asymptotics of realized volatility with non-Gaussian ARCH(∞) microstructure noise

Hiroyuki Taniai, Takashi Usami, Nobuyuki Suto, Masanobu Taniguchi

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    Abstract

    In order to estimate the conditional variance of some specific day, the sum of squared intraday returns, as known as "realized volatility" (RV) or "realized variance," is often used. Although this estimator does not converge to the true volatility when the observed price involves market microstructure noise, some subsample-based estimator is known to resolve this problem. In this paper, we will study the asymptotics of this estimator, assuming that market microstructure noise follows a non-Gaussian autoregressive conditional heteroskedastic model of order ∞ (ARCH(∞)). There we elucidate the asymptotics of RV and subsample estimator, which are influenced by the non-Gaussianity and dependent structure of the noise. Some numerical studies are given, and they illuminate interesting features of the asymptotics.

    Original languageEnglish
    Article numbernbs005
    Pages (from-to)617-636
    Number of pages20
    JournalJournal of Financial Econometrics
    Volume10
    Issue number4
    DOIs
    Publication statusPublished - 2012 Sep

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    Keywords

    • ARCH (∞) model
    • Fourth-order cumulant spectra
    • Market microstructure
    • Realized volatility
    • Statistical asymptotic theory
    • Subsampling

    ASJC Scopus subject areas

    • Economics and Econometrics
    • Finance

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