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27
Power and Bipower Variation with Stochastic Volatility and Jumps
, 2003
"... This paper shows that realised power variation and its extension we introduce here called realised bipower variation is somewhat robust to rare jumps. We show realised bipower variation estimates integrated variance in SV models  thus providing a model free and consistent alternative to realis ..."
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Cited by 145 (21 self)
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This paper shows that realised power variation and its extension we introduce here called realised bipower variation is somewhat robust to rare jumps. We show realised bipower variation estimates integrated variance in SV models  thus providing a model free and consistent alternative to realised variance. Its robustness property means that if we have an SV plus infrequent jumps process then the di#erence between realised variance and realised bipower variation estimates the quadratic variation of the jump component. This seems to be the first method which can divide up quadratic variation into its continuous and jump components. Various extensions are given. Proofs of special cases of these results are given.
Separating microstructure noise from volatility
, 2006
"... There are two variance components embedded in the returns constructed using high frequency asset prices: the timevarying variance of the unobservable efficient returns that would prevail in a frictionless economy and the variance of the equally unobservable microstructure noise. Using sample moment ..."
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Cited by 64 (5 self)
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There are two variance components embedded in the returns constructed using high frequency asset prices: the timevarying variance of the unobservable efficient returns that would prevail in a frictionless economy and the variance of the equally unobservable microstructure noise. Using sample moments of high frequency return data recorded at different frequencies, we provide a simple and robust technique to identify both variance components. In the context of a volatilitytiming trading strategy, we show that careful (optimal) separation of the two volatility components of the observed stock returns yields substantial utility gains.
MICROSTRUCTURE NOISE, REALIZED VARIANCE, AND OPTIMAL SAMPLING
, 2005
"... Observed asset prices are known to deviate from their efficient values due to market microstructure frictions. This paper studies the effects of market microstructure noise on nonparametric estimates of the efficient price integrated variance. Specifically, we consider both asymptotic and finite sam ..."
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Cited by 49 (5 self)
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Observed asset prices are known to deviate from their efficient values due to market microstructure frictions. This paper studies the effects of market microstructure noise on nonparametric estimates of the efficient price integrated variance. Specifically, we consider both asymptotic and finite sample effects of general market microstructure noise on realized variance estimates. The finite sample results culminate in a variance/bias tradeoff that serves as a basis for an optimal sampling theory. Our theory also considers the effects of prefiltering the data and proposes a novel biascorrection. We show that this theory is easily implementable in practise requiring only the calculation of sample moments of the observable highfrequency return data.
A central limit theorem for realised power and bipower variations of continuous semimartingales
 In
, 2006
"... Summary. Consider a semimartingale of the form Yt = Y0 + ∫ t 0 asds + ∫ t σs − dWs, 0 where a is a locally bounded predictable process and σ (the “volatility”) is an adapted right–continuous process with left limits and W is a Brownian motion. We consider the realised bipower variation process V (Y; ..."
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Cited by 38 (17 self)
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Summary. Consider a semimartingale of the form Yt = Y0 + ∫ t 0 asds + ∫ t σs − dWs, 0 where a is a locally bounded predictable process and σ (the “volatility”) is an adapted right–continuous process with left limits and W is a Brownian motion. We consider the realised bipower variation process V (Y; r, s) n t = n r+s
Multivariate realised kernels: consistent positive semidefinite estimators of the covariation of equity prices with noise and nonsynchronous trading
, 2008
"... ..."
BOOTSTRAPPING REALIZED VOLATILITY
 SUBMITTED TO ECONOMETRICA
"... We propose bootstrap methods for a general class of nonlinear transformations of realized volatility which includes the raw version of realized volatility and its logarithmic transformation as special cases. We consider the i.i.d. bootstrap and the wild bootstrap (WB) and prove their firstorder asy ..."
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Cited by 20 (3 self)
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We propose bootstrap methods for a general class of nonlinear transformations of realized volatility which includes the raw version of realized volatility and its logarithmic transformation as special cases. We consider the i.i.d. bootstrap and the wild bootstrap (WB) and prove their firstorder asymptotic validity under general assumptions on the logprice process that allow for drift and leverage effects. We derive Edgeworth expansions in a simpler model that rules out these effects. The i.i.d. bootstrap provides a secondorder asymptotic refinement when volatility is constant, but not otherwise. The WB yields a secondorder asymptotic refinement under stochastic volatility provided we choose the external random variable used to construct the WB data appropriately. None of these methods provide thirdorder asymptotic refinements. Both methods improve upon the firstorder asymptotic theory in finite samples.
Power Variation & Stochastic Volatility: a review and some new results
, 2003
"... In this paper we review some recent work on limit results on realised power variation, that is sums of powers of absolute increments of various semimartingales. A special case of this analysis is realised variance and its probability limit, quadratic variation. Such quantities often appear in fin ..."
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Cited by 15 (2 self)
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In this paper we review some recent work on limit results on realised power variation, that is sums of powers of absolute increments of various semimartingales. A special case of this analysis is realised variance and its probability limit, quadratic variation. Such quantities often appear in financial econometrics in the analysis of volatility. The paper also provides some new results and discusses open issues.
Impact of Jumps on Returns and Realised Variances: Econometric analysis of timedeformed Lévy processes
 Journal of Econometrics
, 2004
"... In order to assess the e#ect of jumps on realised variance calculations, we study some of the econometric properties of timechanged Levy processes. We show that in general realised variance is an inconsistent estimator of the timechange, however we can derive the second order properties of real ..."
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Cited by 13 (11 self)
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In order to assess the e#ect of jumps on realised variance calculations, we study some of the econometric properties of timechanged Levy processes. We show that in general realised variance is an inconsistent estimator of the timechange, however we can derive the second order properties of realised variances and use these to estimate the parameters of such models. Our analytic results give a first indication of the degrees of inconsistency of realised variance as an estimator of the timechange in the nonBrownian case. Further, our results suggest volatility is even more predictable than has been shown by the recent econometric work on realised variance.
Realising the future: forecasting with high frequency based volatility (HEAVY) models
, 2009
"... This paper studies in some detail a class of high frequency based volatility (HEAVY) models. These models are direct models of daily asset return volatility based on realized measures constructed from high frequency data. Our analysis identifies that the models have momentum and mean reversion effec ..."
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Cited by 12 (1 self)
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This paper studies in some detail a class of high frequency based volatility (HEAVY) models. These models are direct models of daily asset return volatility based on realized measures constructed from high frequency data. Our analysis identifies that the models have momentum and mean reversion effects, and that they adjust quickly to structural breaks in the level of the volatility process. We study how to estimate the models and how they perform through the credit crunch, comparing their fit to more traditional GARCH models. We analyse a model based bootstrap which allow us to estimate the entire predictive distribution of returns. We also provide an analysis of missing data in the context of these models.