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Estimating quadratic variation using realized variance
Author(s) -
BarndorffNielsen Ole E.,
Shephard Neil
Publication year - 2002
Publication title -
journal of applied econometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.878
H-Index - 99
eISSN - 1099-1255
pISSN - 0883-7252
DOI - 10.1002/jae.691
Subject(s) - semimartingale , quadratic variation , estimator , econometrics , realized variance , mathematics , variance (accounting) , quadratic equation , volatility (finance) , economics , statistics , brownian motion , geometry , accounting
This paper looks at some recent work on estimating quadratic variation using realized variance (RV)—that is, sums of M squared returns. This econometrics has been motivated by the advent of the common availability of high‐frequency financial return data. When the underlying process is a semimartingale we recall the fundamental result that RV is a consistent (as M → ∞) estimator of quadratic variation (QV). We express concern that without additional assumptions it seems difficult to give any measure of uncertainty of the RV in this context. The position dramatically changes when we work with a rather general SV model—which is a special case of the semimartingale model. Then QV is integrated variance and we can derive the asymptotic distribution of the RV and its rate of convergence. These results do not require us to specify a model for either the drift or volatility functions, although we have to impose some weak regularity assumptions. We illustrate the use of the limit theory on some exchange rate data and some stock data. We show that even with large values of M the RV is sometimes a quite noisy estimator of integrated variance. Copyright © 2002 John Wiley & Sons, Ltd.