Realized range-based estimation of integrated variance

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    Abstract

    We provide a set of probabilistic laws for estimating the quadratic variation of continuous semimartingales with the realized range-based variance-a statistic that replaces every squared return of the realized variance with a normalized squared range. If the entire sample path of the process is available, and under a set of weak conditions, our statistic is consistent and has a mixed Gaussian limit, whose precision is five times greater than that of the realized variance. In practice, of course, inference is drawn from discrete data and true ranges are unobserved, leading to downward bias. We solve this problem to get a consistent, mixed normal estimator, irrespective of non-trading effects. This estimator has varying degrees of efficiency over realized variance, depending on how many observations that are used to construct the high-low. The methodology is applied to TAQ data and compared with realized variance. Our findings suggest that the empirical path of quadratic variation is also estimated better with the realized range-based variance.
    Original languageEnglish
    JournalJournal of Econometrics
    Volume141
    Issue2
    Pages (from-to)323-349
    Number of pages27
    ISSN0304-4076
    DOIs
    Publication statusPublished - 2007

    Keywords

    • Central limit theorem
    • Continuous semimartingales
    • Integrated variance
    • Realized range-based variance
    • Realized variance

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