Realized Volatility When Sampling Times are Possibly Endogenous

Li, Yingying; Mykland, Per A.; Renault, Éric; Zhang, Lan; Zheng, Xinghua

doi:10.2139/ssrn.1525410

Cited by 25 publications

(33 citation statements)

References 56 publications

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“…A treatment of endogenous times in the given theoretical framework is beyond the scope of this paper. See Koike (2016) for a recent study of endogenous times and Li et al (2014) for a study in a setting neglecting microstructure noise.…”

Section: Theoretical Setup and Assumptionsmentioning

confidence: 99%

Estimating the Spot Covariation of Asset Prices Statistical Theory and Empirical Evidence

et al. 2014

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We propose a new estimator for the spot covariance matrix of a multi-dimensional continuous semi-martingale log asset price process which is subject to noise and non-synchronous observations. The estimator is constructed based on a local average of block-wise para-metric spectral covariance estimates. The latter originate from a local method of moments (LMM) which recently has been introduced by Bibinger et al. (2014). We prove consistency and a point-wise stable central limit theorem for the proposed spot covariance estimator in a very general setup with stochastic volatility, leverage effects and general noise distributions. Moreover, we extend the LMM estimator to be robust against autocorrelated noise and propose a method to adaptively infer the autocorrelations from the data. Based on simulations we provide empirical guidance on the effective implementation of the estimator and apply it to high-frequency data of a cross-section of Nasdaq blue chip stocks. Employing the estimator to estimate spot covariances, correlations and volatilities in normal but also unusual periods yields novel insights into intraday covariance and correlation dynamics. We show that intraday (co-)variations (i) follow underlying periodicity patterns, (ii) reveal substantial intraday variability associated with (co-)variation risk, and (iii) can increase strongly and nearly instantaneously if new information arrives.

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Section: Theoretical Setup and Assumptionsmentioning

confidence: 99%

Estimating the Spot Covariation of Asset Prices Statistical Theory and Empirical Evidence

et al. 2014

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“…This situation arises, for example, in the case of endogenous sampling times for realized volatility (Li, Mykland, Renault, Zhang, and Zheng (2014)). The same phenomenon occurs under direct estimation of skewness (Kinnebrock and Podolskij (2008, Example 6); Mykland and Zhang (2009, Example 3, pp.…”

Section: Qedmentioning

confidence: 99%

Assessment of Uncertainty in High Frequency Data: The Observed Asymptotic Variance

Mykland¹,

Zhang²

2017

Econometrica

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The availability of high frequency financial data has generated a series of estimators based on intra‐day data, improving the quality of large areas of financial econometrics. However, estimating the standard error of these estimators is often challenging. The root of the problem is that traditionally, standard errors rely on estimating a theoretically derived asymptotic variance, and often this asymptotic variance involves substantially more complex quantities than the original parameter to be estimated. Standard errors are important: they are used to assess the precision of estimators in the form of confidence intervals, to create “feasible statistics” for testing, to build forecasting models based on, say, daily estimates, and also to optimize the tuning parameters. The contribution of this paper is to provide an alternative and general solution to this problem, which we call Observed Asymptotic Variance. It is a general nonparametric method for assessing asymptotic variance (AVAR). It provides consistent estimators of AVAR for a broad class of integrated parameters Θ = ∫ θt dt, where the spot parameter process θ can be a general semimartingale, with continuous and jump components. The observed AVAR is implemented with the help of a two‐scales method. Its construction works well in the presence of microstructure noise, and when the observation times are irregular or asynchronous in the multivariate case. The methodology is valid for a wide variety of estimators, including the standard ones for variance and covariance, and also for more complex estimators, such as, of leverage effects, high frequency betas, and semivariance.

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“…See Koike (2016) for a recent study of endogenous times and Li et al (2014) for a study in a setting neglecting microstructure noise.…”

Section: Theoretical Setup and Assumptionsmentioning

confidence: 99%

Estimating the Spot Covariation of Asset Prices Statistical Theory and Empirical Evidence

et al. 2014

View full text Add to dashboard Cite

We propose a new estimator for the spot covariance matrix of a multi-dimensional continuous semi-martingale log asset price process which is subject to noise and non-synchronous observations. The estimator is constructed based on a local average of block-wise parametric spectral covariance estimates. The latter originate from a local method of moments (LMM) which recently has been introduced by . We prove consistency and a point-wise stable central limit theorem for the proposed spot covariance estimator in a very general setup with stochastic volatility, leverage effects and general noise distributions.Moreover, we extend the LMM estimator to be robust against autocorrelated noise and propose a method to adaptively infer the autocorrelations from the data. Based on simulations we provide empirical guidance on the effective implementation of the estimator and apply it to high-frequency data of a cross-section of Nasdaq blue chip stocks. Employing the estimator to estimate spot covariances, correlations and volatilities in normal but also unusual periods yields novel insights into intraday covariance and correlation dynamics.We show that intraday (co-)variations (i) follow underlying periodicity patterns, (ii) reveal substantial intraday variability associated with (co-)variation risk, and (iii) can increase strongly and nearly instantaneously if new information arrives.

show abstract

Realized Volatility When Sampling Times are Possibly Endogenous

Cited by 25 publications

References 56 publications

Estimating the Spot Covariation of Asset Prices Statistical Theory and Empirical Evidence

Estimating the Spot Covariation of Asset Prices Statistical Theory and Empirical Evidence

Assessment of Uncertainty in High Frequency Data: The Observed Asymptotic Variance

Estimating the Spot Covariation of Asset Prices Statistical Theory and Empirical Evidence

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