Rasmus T. Varneskov

Estimating the quadratic variation spectrum of noisy asset prices using generalized flat-top realized kernels

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This paper analyzes a generalized class of flat-top realized kernel estimators for the quadratic variation spectrum, that is, the decomposition of quadratic variation into integrated variance and jump variation. The underlying log-price process is contaminated by additive noise, which consists of two orthogonal components to accommodate alpha-mixing dependent exogenous noise and an asymptotically non-degenerate endogenous correlation structure. In the absence of jumps, the class of estimators is shown to be consistent, asymptotically unbiased, and mixed Gaussian at the optimal rate of convergence, n(1/4). Exact bounds on lower-order terms are obtained, and these are used to propose a selection rule for the flat-top shrinkage. Bounds on the optimal bandwidth for noise models of varying complexity are also provided. In theoretical and numerical comparisons with alternative estimators, including the realized kernel, the two-scale realized kernel, and a bias-corrected pre-averaging estimator, the flat-top realized kernel enjoys a higher-order advantage in terms of bias reduction, in addition to good efficiency properties. The analysis is extended to jump-diffusions where the asymptotic properties of a flat-top realized kernel estimate of the total quadratic variation are established. Apart from a larger asymptotic variance, they are similar to the no-jump case. Finally, the estimators are used to design two classes of (medium) blocked realized kernels, which produce consistent, non-negative estimates of integrated variance. The blocked estimators are shown to have no loss either of asymptotic efficiency or in the rate of consistency relative to the flat-top realized kernels when jumps are absent. However, only the medium blocked realized kernels achieve the optimal rate of convergence under the jump alternative.

Original languageEnglish
JournalEconometric Theory
Volume33
Issue6
Pages (from-to)1457-1501
Number of pages45
ISSN0266-4666
DOIs
Publication statusPublished - Dec 2017

    Research areas

  • HIGH-FREQUENCY DATA, STOCHASTIC VOLATILITY MODELS, MARKET MICROSTRUCTURE NOISE, STATIONARY TIME-SERIES, COVARIANCE-MATRIX, JUMPS, INFERENCE, VARIANCE, SEMIMARTINGALES, COMPONENTS

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