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

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Estimating the quadratic variation spectrum of noisy asset prices using generalized flat-top realized kernels. / Varneskov, Rasmus Tangsgaard.

In: Econometric Theory, Vol. 33, No. 6, 12.2017, p. 1457-1501.

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@article{4587e9e05dd94e5bbaf21d1cb12ccdd9,
title = "Estimating the quadratic variation spectrum of noisy asset prices using generalized flat-top realized kernels",
abstract = "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.",
keywords = "HIGH-FREQUENCY DATA, STOCHASTIC VOLATILITY MODELS, MARKET MICROSTRUCTURE NOISE, STATIONARY TIME-SERIES, COVARIANCE-MATRIX, JUMPS, INFERENCE, VARIANCE, SEMIMARTINGALES, COMPONENTS",
author = "Varneskov, {Rasmus Tangsgaard}",
year = "2017",
month = dec,
doi = "10.1017/S0266466616000475",
language = "English",
volume = "33",
pages = "1457--1501",
journal = "Econometric Theory",
issn = "0266-4666",
publisher = "Cambridge University Press",
number = "6",

}

RIS

TY - JOUR

T1 - Estimating the quadratic variation spectrum of noisy asset prices using generalized flat-top realized kernels

AU - Varneskov, Rasmus Tangsgaard

PY - 2017/12

Y1 - 2017/12

N2 - 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.

AB - 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.

KW - HIGH-FREQUENCY DATA

KW - STOCHASTIC VOLATILITY MODELS

KW - MARKET MICROSTRUCTURE NOISE

KW - STATIONARY TIME-SERIES

KW - COVARIANCE-MATRIX

KW - JUMPS

KW - INFERENCE

KW - VARIANCE

KW - SEMIMARTINGALES

KW - COMPONENTS

U2 - 10.1017/S0266466616000475

DO - 10.1017/S0266466616000475

M3 - Journal article

VL - 33

SP - 1457

EP - 1501

JO - Econometric Theory

JF - Econometric Theory

SN - 0266-4666

IS - 6

ER -