Edgeworth expansions for realized volatility and related estimators

Zhang, Lan; Mykland, Per A.; Aı̈t-Sahalia, Yacine

doi:10.1016/j.jeconom.2010.03.030

Cited by 39 publications

(8 citation statements)

References 45 publications

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“…Goncalves and Meddahi (2004) and Zhang, Mykland, and Aït-Sahalia (2005a) have studied Edgeworth expansions of these types of results, while the former also derived a bootstrapped version to improve the finite sample performance of the feasible version of the theory.…”

Section: Commentsmentioning

confidence: 99%

Subsampling realised kernels

Barndorff–Nielsen

Hansen

Lunde

et al. 2011

Journal of Econometrics

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In a recent paper we have introduced the class of realised kernel estimators of the increments of quadratic variation in the presence of noise. We showed that this estimator is consistent and derived its limit distribution under various assumptions on the kernel weights. In this paper we extend our analysis, looking at the class of subsampled realised kernels and we derive the limit theory for this class of estimators. We find that subsampling is highly advantageous for estimators based on discontinuous kernels, such as the truncated kernel. For kinked kernels, such as the Bartlett kernel, we show that subsampling is impotent, in the sense that subsampling has no effect on the asymptotic distribution. Perhaps surprisingly, for the efficient smooth kernels, such as the Parzen kernel, we show that subsampling is harmful as it increases the asymptotic variance. We also study the performance of subsampled realised kernels in simulations and in empirical work.

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Section: Commentsmentioning

confidence: 99%

Subsampling realised kernels

Barndorff–Nielsen

Hansen

Lunde

et al. 2011

Journal of Econometrics

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“…By Withers and Nadarajah (2012), the expansions (1.5)-(1.7), (1.9)-(1.11) remain true for 21) and p X (x) = p(x) is the density of X, if…”

Section: Introductionmentioning

confidence: 97%

“…The Cornish Fisher expansions also have applications in many applied areas, including risk measures for hedge funds, margin setting of index futures, structural equation models, modified sudden death tests, blind inversion of Wiener systems, GPS positioning accuracy estimation, steady-state simulation analysis, blind separation of post-nonlinear mixtures, cycle time quantile estimation, estimation of the maximum average time to flower, performance of Skart, testing and evaluation, load flow in systems with wind generation, Value-at-Risk portfolio optimization, quantile mechanics, channel capacity in communications theory, economics, financial intermediation and physics. Three of the most recent papers applying Cornish Fisher expansions to these areas are: Alfredo and Arunachalam (2011), Simonato (2011) and Zhang et al (2011).…”

Section: Introductionmentioning

confidence: 99%

Expansions about the Gamma for the Distribution and Quantiles of a Standard Estimate

Withers¹,

Nadarajah

2013

Methodol Comput Appl Probab

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We give expansions for the distribution, density, and quantiles of an estimate, building on results of Cornish, Fisher, Hill, Davis and the authors. The estimate is assumed to be non-lattice with the standard expansions for its cumulants. By expanding about a skew variable with matched skewness, one can drastically reduce the number of terms needed for a given level of accuracy. The building blocks generalize the Hermite polynomials. We demonstrate with expansions about the gamma.

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“…The bootstrap could also be useful for inference in the context of these estimators. Indeed, Zhang et al (2011) showed that the asymptotic normal approximation is often inaccurate for the subsampling realized volatility estimator, whose finite sample distribution is skewed and heavy tailed. They proposed Edgeworth corrections for this estimator as a way to improve upon the standard normal approximation.…”

Section: Introductionmentioning

confidence: 99%

Bootstrapping Pre-Averaged Realized Volatility Under Market Microstructure Noise

2016

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The main contribution of this paper is to propose a bootstrap method for inference on integrated volatility based on the pre-averaging approach of Jacod et al. (2009), where the pre-averaging is done over all possible overlapping blocks of consecutive observations. The overlapping nature of the pre-averaged returns implies that these are k n -dependent with k n growing slowly with the sample size n. This motivates the application of a blockwise bootstrap method. We show that the "blocks of blocks" bootstrap method suggested by Politis and Romano (1992) (and further studied by Bühlmann and Künsch (1995)) is valid only when volatility is constant. The failure of the blocks of blocks bootstrap is due to the heterogeneity of the squared pre-averaged returns when volatility is stochastic. To preserve both the dependence and the heterogeneity of squared pre-averaged returns, we propose a novel procedure that combines the wild bootstrap with the blocks of blocks bootstrap. We provide a proof of the first order asymptotic validity of this method for percentile intervals. Our Monte Carlo simulations show that the wild blocks of blocks bootstrap improves the finite sample properties of the existing first order asymptotic theory. We use empirical work to illustrate its use in practice.

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Edgeworth expansions for realized volatility and related estimators

Cited by 39 publications

References 45 publications

Subsampling realised kernels

Subsampling realised kernels

Expansions about the Gamma for the Distribution and Quantiles of a Standard Estimate

Bootstrapping Pre-Averaged Realized Volatility Under Market Microstructure Noise

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