Estimation of Volatility Functionals in the Simultaneous Presence of Microstructure Noise and Jumps

Podolskij, Mark; Vetter, Mathias; Sommer, Margit

doi:10.2139/ssrn.950344

Cited by 63 publications

(83 citation statements)

References 42 publications

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“…This idea is widely adopted in various extensions. See , Podolskij and Vetter (2009), Christensen et al (2010Christensen et al ( , 2017, Andersen et al (2012), Christensen and Podolskij (2012), Barunik and Vacha (2015), and Mykland and Zhang (2017), etc. (2) The truncation method (Mancini, 2008(Mancini, , 2011, which discards relatively large returns in RV summation terms, and 755 variables.…”

Section: Introductionmentioning

confidence: 99%

Volatility Estimation and Jump Testing via Realized Information Variation

Liu

Wang

2019

Journal Time Series Analysis

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We put forward a new method to construct jump‐robust estimators of integrated volatility, namely realized information variation (RIV) and realized information power variation (RIPV). The ‘information’ here refers to the difference between two‐grid of ranges in high‐frequency intervals, which preserves continuous variation and eliminates jump variation asymptotically. We show that such kind of estimators have several superior statistical properties, i.e., the estimators are generally more efficient with sufficiently using the opening, high, low, closing (OHLC) data in high‐frequency intervals, and have faster jump convergence rate due to a new type of construction. For example, the RIV is much more efficient than the estimators that only use closing prices or ranges, and the RIPV has faster jump convergence rate at Op(1/n), while the other (multi)power‐based estimators are usually Opfalse(1false/nfalse). We also extend our results to integrated quarticity and higher‐order variation estimation, and then propose the corresponding jump testing method. Simulation studies provide extensive evidence on the finite sample properties of our estimators and tests, comparing with alternative prevalent methods. Empirical results further demonstrate the practical relevance and advantages of our method.

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Section: Introductionmentioning

confidence: 99%

Volatility Estimation and Jump Testing via Realized Information Variation

Liu

Wang

2019

Journal Time Series Analysis

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“…In the context of volatility estimation, several methods to de-noise the data have been proposed. Widely used methods include the two-scale method ), the multi-scale method (Zhang (2006)), the realized kernel method (Barndorff-Nielsen, Hansen, Lunde, and Shephard (2008)), the pre-averaging method (Jacod, Li, Mykland, Podolskij, and Vetter (2009) and Podolskij and Vetter (2009)), and the quasi-maximum likelihood method (Xiu (2010)). These methods are shown to be effective when the noise is an additive white noise, or admits some kind of independence between successive observations.…”

Section: Introductionmentioning

confidence: 99%

Statistical Properties of Microstructure Noise

Jacod

Zheng

2017

Econometrica

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We study the estimation of (joint) moments of microstructure noise based on high frequency data. The estimation is conducted under a nonparametric setting, which allows the underlying price process to have jumps, the observation times to be irregularly spaced, and the noise to be dependent on the price process and to have diurnal features. Estimators of arbitrary orders of (joint) moments are provided, for which we establish consistency as well as central limit theorems. In particular, we provide estimators of autocovariances and autocorrelations of the noise. Simulation studies demonstrate excellent performance of our estimators in the presence of jumps, irregular observation times, and even rounding. Empirical studies reveal (moderate) positive autocorrelations of microstructure noise for the stocks tested.

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“…Then, we suggest a new optimal external random variable with a density that yields the second-order accuracy of the bootstrap. Gonçalves et al (2014) have shown that the wild bootstrap procedure applied on the nonoverlapping pre-averaged returns (as originally proposed by Podolskij and Vetter, 2009) estimates the asymptotic variance as well as the asymptotic mixed normal distribution of the pre-averaged realized volatility estimator. However, for this relatively simple statistic, we can simply use, for instance, the consistent variance estimator proposed by Podolskij and Vetter (2009).…”

Section: Introductionmentioning

confidence: 99%

“…Gonçalves et al (2014) have shown that the wild bootstrap procedure applied on the nonoverlapping pre-averaged returns (as originally proposed by Podolskij and Vetter, 2009) estimates the asymptotic variance as well as the asymptotic mixed normal distribution of the pre-averaged realized volatility estimator. However, for this relatively simple statistic, we can simply use, for instance, the consistent variance estimator proposed by Podolskij and Vetter (2009). Hence, the additional effort required for the bootstrap is justified if the resulting approximation to the distribution of the statistic is better than the one relying on the asymptotic normality.…”

Section: Introductionmentioning

confidence: 99%

Validity of Edgeworth expansions for realized volatility estimators

Hounyo

Veliyev

2016

The Econometrics Journal

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The main contribution of this paper is to establish the formal validity of Edgeworth expansions for realized volatility estimators. First, in the context of no microstructure effects, our results rigorously justify the Edgeworth expansions for realized volatility derived in Gonçalves and Meddahi (2009, Econometrica 77, 283-306). Second, we show that the validity of the Edgeworth expansions for realized volatility might not cover the optimal two-point distribution wild bootstrap proposed by Gonçalves and Meddahi. Then, we propose a new optimal nonlattice distribution, which ensures the second-order correctness of the bootstrap. Third, in the presence of microstructure noise, based on our Edgeworth expansions, we show that the new optimal choice proposed in the absence of noise is still valid in noisy data for the pre-averaged realized volatility estimator proposed by Podolskij and Vetter (2009, Bernoulli 15, 634-658). Finally, we show how confidence intervals for integrated volatility can be constructed using these Edgeworth expansions for noisy data. Our Monte Carlo simulations show that the intervals based on the Edgeworth corrections have improved the finite sample properties relatively to the conventional intervals based on the normal approximation.

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Estimation of Volatility Functionals in the Simultaneous Presence of Microstructure Noise and Jumps

Cited by 63 publications

References 42 publications

Volatility Estimation and Jump Testing via Realized Information Variation

Volatility Estimation and Jump Testing via Realized Information Variation

Statistical Properties of Microstructure Noise

Validity of Edgeworth expansions for realized volatility estimators

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