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Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise

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Author Info
Neil Shephard
Ole E. Barndorff-Nielsen
Peter Reinhard Hansen
Asger Lunde

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Abstract

This paper shows how to use realised kernels to carry out efficient feasible inference on the ex-post variation of underlying equity prices in the presence of simple models of market frictions. The issue is subtle with only estimators which have symmetric weights delivering consistent estimators with mixed Gaussian limit theorems. The weights can be chosen to achieve the best possible rate of convergence and to have an asymptotic variance which is close to that of the maximum likelihood estimator in the parametric version of this problem. Realised kernels can also be selected to (i) be analysed using endogenously spaced data such as that in databases on transactions, (ii) allow for market frictions which are endogenous, (iii) allow for temporally dependent noise. The finite sample performance of our estimators is studied using simulation, while empirical work illustrates their use in practice.

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Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 264.

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Date of creation: 2006
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Handle: RePEc:oxf:wpaper:264

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Keywords: Bipower Variation Long Run Variance Estimator Market Frictions Quadratic Variation Realised Variance

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models

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