Results 1  10
of
30
Ultra high frequency volatility estimation with dependent microstructure noise
"... We analyze the impact of time series dependence in market microstructure noise on the properties of estimators of the integrated volatility of an asset price based on data sampled at frequencies high enough for that noise to be a dominant consideration. We show that combining two time scales for tha ..."
Abstract

Cited by 100 (11 self)
 Add to MetaCart
We analyze the impact of time series dependence in market microstructure noise on the properties of estimators of the integrated volatility of an asset price based on data sampled at frequencies high enough for that noise to be a dominant consideration. We show that combining two time scales for that purpose will work even when the noise exhibits time series dependence, analyze in that context a refinement of this approach based on multiple time scales, and compare empirically our different estimators to the standard realized volatility.
Microstructure noise in the continuous case: the preaveraging approach’,
 Stochastic Processes and their Applications 119,
, 2009
"... Abstract This paper presents a generalized preaveraging approach for estimating the integrated volatility, in the presence of noise. This approach also provides consistent estimators of other powers of volatility in particular, it gives feasible ways to consistently estimate the asymptotic varian ..."
Abstract

Cited by 95 (18 self)
 Add to MetaCart
(Show Context)
Abstract This paper presents a generalized preaveraging approach for estimating the integrated volatility, in the presence of noise. This approach also provides consistent estimators of other powers of volatility in particular, it gives feasible ways to consistently estimate the asymptotic variance of the estimator of the integrated volatility. We show that our approach, which possesses an intuitive transparency, can generate rate optimal estimators (with convergence rate n −1/4 ).
Volatility Forecast Comparison Using Imperfect Volatility Proxies
 JOURNAL OF ECONOMETRICS
, 2010
"... ..."
Inference for Continuous Semimartingales Observed at High Frequency: A General Approach
, 2008
"... The econometric literature of high frequency data often relies on moment estimators which are derived from assuming local constancy of volatility and related quantities. We here study this localconstancy approximation as a general approach to estimation in such data. We show that the technique yiel ..."
Abstract

Cited by 44 (11 self)
 Add to MetaCart
The econometric literature of high frequency data often relies on moment estimators which are derived from assuming local constancy of volatility and related quantities. We here study this localconstancy approximation as a general approach to estimation in such data. We show that the technique yields asymptotic properties (consistency, normality) that are correct subject to an ex post adjustment involving asymptotic likelihood ratios. These adjustments are given. Several examples of estimation are provided: powers of volatility, leverage effect, integrated betas, bipower, and covariance under asynchronous observation. The first order approximations in this study can be over the period of one observation, or over blocks of successive observations. The advantage of blocking is a gain in transparency in defining and analyzing estimators. The theory relies heavily on the interplay between stable convergence and measure change, and on asymptotic expansions for martingales.
Edgeworth expansions for realized volatility and related estimators
, 2005
"... This paper shows that the asymptotic normal approximation is often insufficiently accurate for volatility estimators based on high frequency data. To remedy this, we derive Edgeworth expansions for such estimators. The expansions are developed in the framework of smallnoise asymptotics. The results ..."
Abstract

Cited by 22 (4 self)
 Add to MetaCart
This paper shows that the asymptotic normal approximation is often insufficiently accurate for volatility estimators based on high frequency data. To remedy this, we derive Edgeworth expansions for such estimators. The expansions are developed in the framework of smallnoise asymptotics. The results have application to CornishFisher inversion and help setting intervals more accurately than those relying on normal distribution.
A Gaussian calculus for inference from high frequency data
, 2006
"... In the econometric literature of high frequency data, it is often assumed that one can carry out inference conditionally on the underlying volatility processes. In other words, conditionally Gaussian systems are considered. This is often referred to as the assumption of “no leverage effect”. This is ..."
Abstract

Cited by 19 (4 self)
 Add to MetaCart
In the econometric literature of high frequency data, it is often assumed that one can carry out inference conditionally on the underlying volatility processes. In other words, conditionally Gaussian systems are considered. This is often referred to as the assumption of “no leverage effect”. This is often a reasonable thing to do, as general estimators and results can often be conjectured from considering the conditionally Gaussian case. The purpose of this paper is to try to give some more structure to the things one can do with the Gaussian assumption. We shall argue in the following that there is a whole treasure chest of tools that can be brought to bear on high frequency data problems in this case. We shall in particular consider approximations involving locally constant volatility processes, and develop a general theory for this approximation. As applications of the theory, we propose an improved estimator of quarticity, an ANOVA for processes with multiple regressors, and an estimator for error bars on the HayashiYoshida estimator of quadratic covariation Some key words and phrases: consistency, cumulants, contiguity, continuity, discrete observation, efficiency, Itô process, likelihood inference, realized volatility, stable convergence
Comment on “Realized variance and market microstructure noise" by Peter Hansen and Asger Lunde
, 2005
"... We enjoyed reading the HansenLunde paper (HL thereafter), and are pleased to be able to contribute some comments. We raise some issues which we feel are important. Some of them are ..."
Abstract

Cited by 9 (4 self)
 Add to MetaCart
We enjoyed reading the HansenLunde paper (HL thereafter), and are pleased to be able to contribute some comments. We raise some issues which we feel are important. Some of them are
Bootstrapping realized multivariate volatility measures
"... We study bootstrap methods for statistics that are a function of multivariate high frequency returns such as realized regression coefficients and realized covariances and correlations. For these measures of covariation, the Monte Carlo simulation results of BarndorffNielsen and Shephard (2004) show ..."
Abstract

Cited by 9 (1 self)
 Add to MetaCart
We study bootstrap methods for statistics that are a function of multivariate high frequency returns such as realized regression coefficients and realized covariances and correlations. For these measures of covariation, the Monte Carlo simulation results of BarndorffNielsen and Shephard (2004) show that finite sample distortions associated with their feasible asymptotic theory approach may arise if sampling is not too frequent. This motivates our use of the bootstrap as an alternative tool of inference for covariation measures. We consider an i.i.d. bootstrap applied to the vector of returns. We show that the finite sample performance of the bootstrap is superior to the existing firstorder asymptotic theory. Nevertheless, and contrary to the existing results in the bootstrap literature for regression models subject to heteroskedasticity in the error term, the Edgeworth expansion for the i.i.d. bootstrap that we develop here shows that this method is not second order accurate. We argue that this is due to the fact that the conditional mean parameters of realized regression models are heterogeneous under stochastic volatility.
Integrated volatility and roundoff error
, 2009
"... We consider a microstructure model for a financial asset, allowing for price discreteness and for a diffusive behavior at large sampling scale. This model, introduced by Delattre and Jacod, consists in the observation at the high frequency n, with roundoff error αn, of a diffusion on a finite inter ..."
Abstract

Cited by 8 (4 self)
 Add to MetaCart
We consider a microstructure model for a financial asset, allowing for price discreteness and for a diffusive behavior at large sampling scale. This model, introduced by Delattre and Jacod, consists in the observation at the high frequency n, with roundoff error αn, of a diffusion on a finite interval. We give from this sample estimators for different forms of the integrated volatility of the asset. Our method is based on variational properties of the process associated with wavelet techniques. We prove that the accuracy of our estimation procedures is αn ∨n −1/2. Using compensated estimators, limit theorems are obtained.