Results 1  10
of
38
The Relative Contribution of Jumps to Total Price Variance
 JOURNAL OF FINANCIAL ECONOMETRICS
, 2005
"... We examine tests for jumps based on recent asymptotic results; we interpret the tests as Hausmantype tests. Monte Carlo evidence suggests that the daily ratio zstatistic has appropriate size, good power, and good jump detection capabilities revealed by the confusion matrix comprised of jump classi ..."
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Cited by 162 (6 self)
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We examine tests for jumps based on recent asymptotic results; we interpret the tests as Hausmantype tests. Monte Carlo evidence suggests that the daily ratio zstatistic has appropriate size, good power, and good jump detection capabilities revealed by the confusion matrix comprised of jump classification probabilities. We identify a pitfall in applying the asymptotic approximation over an entire sample. Theoretical and Monte Carlo analysis indicates that microstructure noise biases the tests against detecting jumps, and that a simple lagging strategy corrects the bias. Empirical work documents evidence for jumps that account for 7% of stock market price variance.
Jump robust volatility estimation using nearest neighbor truncation
, 2009
"... We propose two new jumprobust estimators of integrated variance based on highfrequency 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 jumprobust estimators of integrated variance based on highfrequency 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 finitesample 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 jumprobust 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.
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 30 (5 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.
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 smallsample 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.
SemiParametric Comparison of Stochastic Volatility Models using Realized Measures
, 2006
"... This paper proposes a procedure to test for the correct specification of the functional form of the volatility process within the class of eigenfunction stochastic volatility models. The procedure is based on the comparison of the moments of realized volatility measures with the corresponding ones o ..."
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Cited by 24 (3 self)
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This paper proposes a procedure to test for the correct specification of the functional form of the volatility process within the class of eigenfunction stochastic volatility models. The procedure is based on the comparison of the moments of realized volatility measures with the corresponding ones of integrated volatility implied by the model under the null hypothesis. We first provide primitive conditions on the measurement error associated with the realized measure, which allow to construct asymptotically valid specification tests. Then we establish regularity conditions under which the considered realized measures, namely, realized volatility, bipower variation, and modified subsampled realized volatility, satisfy the given primitive assumptions. Finally, we provide an empirical illustration based on three stocks from the Dow Jones Industrial Average.
Positivedefinite matrix processes of finite variation
 Probab. Math. Statist
, 2007
"... Processes of finite variation, which take values in the positive semidefinite matrices and are representable as the sum of an integral with respect to time and one with respect to an extended Poisson random measure, are considered. For such processes we derive conditions for the square root (and the ..."
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Cited by 18 (5 self)
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Processes of finite variation, which take values in the positive semidefinite matrices and are representable as the sum of an integral with respect to time and one with respect to an extended Poisson random measure, are considered. For such processes we derive conditions for the square root (and the rth power with 0 < r < 1) to be of finite variation and obtain integral representations of the square root. Our discussion is based on a variant of the Itô formula for finite variation processes. Moreover, OrnsteinUhlenbeck type processes taking values in the positive semidefinite matrices are introduced and their probabilistic properties are studied.
A fourier transform method for nonparametric estimation of multivariate volatility
 Annals of Statistics
"... We provide a nonparametric method for the computation of instantaneous multivariate volatility for continuous semimartingales, which is based on Fourier analysis. The covolatility is reconstructed as a stochastic function of time by establishing a connection between the Fourier transform of the pr ..."
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Cited by 18 (2 self)
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We provide a nonparametric method for the computation of instantaneous multivariate volatility for continuous semimartingales, which is based on Fourier analysis. The covolatility is reconstructed as a stochastic function of time by establishing a connection between the Fourier transform of the prices process and the Fourier transform of the covolatility process. A nonparametric estimator is derived given a discrete unevenly spaced and asynchronously sampled observations of the asset price processes. The asymptotic properties of the random estimator are studied: namely, consistency in probability uniformly in time and convergence in law to a mixture of Gaussian distributions. 1. Introduction. The
Power variation for Gaussian processes with stationary increments
"... We develop the asymptotic theory for the realised power variation of the processes X = φ • G, where G is a Gaussian process with stationary increments. More specifically, under some mild assumptions on the variance function of the increments of G and certain regularity condition on the path of the p ..."
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Cited by 16 (7 self)
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We develop the asymptotic theory for the realised power variation of the processes X = φ • G, where G is a Gaussian process with stationary increments. More specifically, under some mild assumptions on the variance function of the increments of G and certain regularity condition on the path of the process φ we prove the convergence in probability for the properly normalised realised power variation. Moreover, under a further assumption on the Hölder index of the path of φ, we show an associated stable central limit theorem. The main tool is a general central limit theorem, due essentially to Hu & Nualart (2005), Nualart & Peccati (2005) and Peccati & Tudor (2005), for sequences of random variables which admit a chaos representation.
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 BarndorffNielsen, 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 BarndorffNielsen, 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.
Inference for the Jump Part of Quadratic Variation OF ITO SEMIMARTINGALES
 CREATES RESEARCH PAPER
, 2008
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