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66
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 ..."
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Cited by 100 (11 self)
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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 pre-averaging approach’,
- Stochastic Processes and their Applications 119,
, 2009
"... Abstract This paper presents a generalized pre-averaging 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 ..."
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Cited by 95 (18 self)
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Abstract This paper presents a generalized pre-averaging 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 ).
Estimating covariation: Epps effect and microstructure noise
- Journal of Econometrics, forthcoming
, 2009
"... This paper is about how to estimate the integrated covariance 〈X, Y 〉T of two assets over a fixed time horizon [0, T], when the observations of X and Y are “contaminated ” and when such noisy observations are at discrete, but not synchronized, times. We show that the usual previous-tick covariance e ..."
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Cited by 59 (3 self)
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This paper is about how to estimate the integrated covariance 〈X, Y 〉T of two assets over a fixed time horizon [0, T], when the observations of X and Y are “contaminated ” and when such noisy observations are at discrete, but not synchronized, times. We show that the usual previous-tick covariance estimator is biased, and the size of the bias is more pronounced for less liquid assets. This is an analytic characterization of the Epps effect. We also provide optimal sampling frequency which balances the tradeoff between the bias and various sources of stochastic error terms, including nonsynchronous trading, microstructure noise, and time discretization. Finally, a two-scales covariance estimator is provided which simultaneously cancels (to first order) the Epps effect and the effect of microstructure noise. The gain is demonstrated in data.
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 local-constancy approximation as a general approach to estimation in such data. We show that the technique yiel ..."
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Cited by 44 (11 self)
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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 local-constancy 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.
Jump robust volatility estimation using nearest neighbor truncation
, 2009
"... We propose two new jump-robust estimators of integrated variance based on high-frequency return observations. These MinRV and MedRV estimators provide an attractive alternative to the prevailing bipower and multipower variation measures. Specifically, the MedRV estimator has better theoretical effic ..."
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Cited by 35 (3 self)
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We propose two new jump-robust estimators of integrated variance based on high-frequency return observations. These MinRV and MedRV estimators provide an attractive alternative to the prevailing bipower and multipower variation measures. Specifically, the MedRV estimator has better theoretical efficiency properties than the tripower variation measure and displays better finite-sample robustness to both jumps and the occurrence of “zero” returns in the sample. Unlike the bipower variation measure the new estimator allows for the development of an asymptotic limit theory in the presence of jumps. Finally, it retains the local nature associated with the low order multipower variation measures. This proves essential for alleviating finite sample biases arising from the pronounced intraday volatility pattern which afflict alternative jump-robust estimators based on longer blocks of returns. An empirical investigation of the Dow Jones 30 stocks and an extensive simulation study corroborate the robustness and efficiency properties of the new estimators.
Threshold Bipower Variation and the Impact of Jumps on Volatility Forecasting
, 2010
"... This study reconsiders the role of jumps for volatility forecasting by showing that jumps have a positive and mostly significant impact on future volatility. This result becomes apparent once volatility is separated into its continuous and discontinuous component using estimators which are not only ..."
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Cited by 27 (6 self)
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This study reconsiders the role of jumps for volatility forecasting by showing that jumps have a positive and mostly significant impact on future volatility. This result becomes apparent once volatility is separated into its continuous and discontinuous component using estimators which are not only consistent, but also scarcely plagued by small-sample bias. To this purpose, we introduce the concept of threshold bipower variation, which is based on the joint use of bipower variation and threshold estimation. We show that its generalization (threshold multipower variation) admits a feasible central limit theorem in the presence of jumps and provides less biased estimates, with respect to the standard multipower variation, of the continuous quadratic variation in finite samples. We further provide a new test for jump detection which has substantially more power than tests based on multipower variation. Empirical analysis (on the S&P500 index, individual stocks and US bond yields) shows that the proposed techniques improve significantly the accuracy of volatility forecasts especially in periods following the occurrence of a jump.
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 small-noise asymptotics. The results ..."
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Cited by 22 (4 self)
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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 small-noise asymptotics. The results have application to Cornish-Fisher inversion and help setting intervals more accurately than those relying on normal distribution.
Limit theorems for moving averages of discretized processes plus noise
, 2010
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A note on the central limit theorem for bipower variation of general functions
- Stochastic Processes and Their Applications 118
"... In this paper we present the central limit theorem for general functions of the increments of Brownian semimartingales. This provides a natural extension of the results derived in Barndorff-Nielsen, Graversen, Jacod, Podolskij & Shephard (2006), who showed the central limit theorem for even func ..."
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Cited by 16 (9 self)
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In this paper we present the central limit theorem for general functions of the increments of Brownian semimartingales. This provides a natural extension of the results derived in Barndorff-Nielsen, Graversen, Jacod, Podolskij & Shephard (2006), who showed the central limit theorem for even functions. We prove an infeasible central limit theorem for general functions and state some assumptions under which a feasible version of our results can be obtained. Finally, we present some examples from the literature to which our theory can be applied.
