Department of Economics and Business Economics

Estimating the Quadratic Variation Spectrum of Noisy Asset Prices Using Generalized Flat-top Realized Kernels

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@techreport{adc678ef95e94de7a33441bf94372d7e,
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 kernels for estimation ot the quadratic variation spectrum,i.e. the decomposition of quadratic variation into integrated variance and jump variation, when the underlying, efficient price process is contaminated by addictive noise. The additive noise consists of two orthogonal components, which allows for a-mixing dependent exogenous noise and an asymptoticaly non-degenerate endogenous correlation structure, respectively. Both components may exhibit polynomially decaying autocovariances. In the absence of jumps, the class of flat-top estimators are shown to be consistent, asymptotically unbiased, and mixed Gaussian at the optimal rate of convergence, n1/4. Exact bound on lower order terms are obtained using maximal inequalities and these are used to derive a conservative, MSE-optimal flat-top shrinkage. Additionally, bounds on the optimal bandwidth is provided for noise models of varyng complexity. In theoretical and numerical comparisons with alternative estimators, including the realized kernel, the two-scale realized kernel, and a proposed robust pre-averaging estimator, the flat-top realized kernels are shown to have a higher-order advantage in terms of bias reduction. Extending the analysis to accommodate jumps in the underlying price process, the flat-top realized kernels are used to propose two classes of (medium) blocked realized kernels, which produce consistent, non-negative estimates of integrated variance. The blocked estimators are shown to have either no loss 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 achieves the optimal rate of convergence under the jump alternative.",
keywords = "Bias reduction, Jumps, Nonparametric estimation, Market microstructure noise, Quadratic variation, Blocked realized kernel, Medium blocked realized kernel",
author = "Varneskov, {Rasmus T.}",
year = "2014",
language = "English",
type = "WorkingPaper",

}

RIS

TY - UNPB

T1 - Estimating the Quadratic Variation Spectrum of Noisy Asset Prices Using Generalized Flat-top Realized Kernels

AU - Varneskov, Rasmus T.

PY - 2014

Y1 - 2014

N2 - This paper analyzes a generalized class of flat-top realized kernels for estimation ot the quadratic variation spectrum,i.e. the decomposition of quadratic variation into integrated variance and jump variation, when the underlying, efficient price process is contaminated by addictive noise. The additive noise consists of two orthogonal components, which allows for a-mixing dependent exogenous noise and an asymptoticaly non-degenerate endogenous correlation structure, respectively. Both components may exhibit polynomially decaying autocovariances. In the absence of jumps, the class of flat-top estimators are shown to be consistent, asymptotically unbiased, and mixed Gaussian at the optimal rate of convergence, n1/4. Exact bound on lower order terms are obtained using maximal inequalities and these are used to derive a conservative, MSE-optimal flat-top shrinkage. Additionally, bounds on the optimal bandwidth is provided for noise models of varyng complexity. In theoretical and numerical comparisons with alternative estimators, including the realized kernel, the two-scale realized kernel, and a proposed robust pre-averaging estimator, the flat-top realized kernels are shown to have a higher-order advantage in terms of bias reduction. Extending the analysis to accommodate jumps in the underlying price process, the flat-top realized kernels are used to propose two classes of (medium) blocked realized kernels, which produce consistent, non-negative estimates of integrated variance. The blocked estimators are shown to have either no loss 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 achieves the optimal rate of convergence under the jump alternative.

AB - This paper analyzes a generalized class of flat-top realized kernels for estimation ot the quadratic variation spectrum,i.e. the decomposition of quadratic variation into integrated variance and jump variation, when the underlying, efficient price process is contaminated by addictive noise. The additive noise consists of two orthogonal components, which allows for a-mixing dependent exogenous noise and an asymptoticaly non-degenerate endogenous correlation structure, respectively. Both components may exhibit polynomially decaying autocovariances. In the absence of jumps, the class of flat-top estimators are shown to be consistent, asymptotically unbiased, and mixed Gaussian at the optimal rate of convergence, n1/4. Exact bound on lower order terms are obtained using maximal inequalities and these are used to derive a conservative, MSE-optimal flat-top shrinkage. Additionally, bounds on the optimal bandwidth is provided for noise models of varyng complexity. In theoretical and numerical comparisons with alternative estimators, including the realized kernel, the two-scale realized kernel, and a proposed robust pre-averaging estimator, the flat-top realized kernels are shown to have a higher-order advantage in terms of bias reduction. Extending the analysis to accommodate jumps in the underlying price process, the flat-top realized kernels are used to propose two classes of (medium) blocked realized kernels, which produce consistent, non-negative estimates of integrated variance. The blocked estimators are shown to have either no loss 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 achieves the optimal rate of convergence under the jump alternative.

KW - Bias reduction

KW - Jumps

KW - Nonparametric estimation

KW - Market microstructure noise

KW - Quadratic variation

KW - Blocked realized kernel

KW - Medium blocked realized kernel

M3 - Working paper

BT - Estimating the Quadratic Variation Spectrum of Noisy Asset Prices Using Generalized Flat-top Realized Kernels

ER -