We derive the asymptotic efficiency bound for regular estimates of the slope coefficient in a linear continuous-time regression model for the continuous martingale parts of two Itô semimartingales observed on a fixed time interval with asymptotically shrinking mesh of the observation grid. We further construct an estimator from high-frequency data that achieves this efficiency bound and, indeed, is adaptive to the presence of infinite-dimensional nuisance components. The estimator is formed by taking optimal weighted average of local nonparametric volatility estimates that are constructed over blocks of high-frequency observations. To study the asymptotic behavior of the proposed estimator, we introduce a general spatial localization procedure which extends known results on the estimation of integrated volatility functionals to more general classes of functions of volatility. Empirically relevant numerical examples illustrate that the proposed efficient estimator provides nontrivial improvement over alternatives in the extant literature.
|Original language||English (US)|
|Number of pages||31|
|State||Published - Jan 11 2016|