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72
Testing for Jumps in a Discretely Observed Process
 ANNALS OF STATISTICS
, 2009
"... We propose a new test to determine whether jumps are present in asset returns or other discretely sampled processes. As the sampling interval tends to 0, our test statistic converges to 1 if there are jumps, and to another deterministic and known value (such as 2) if there are no jumps. The test is ..."
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Cited by 67 (4 self)
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We propose a new test to determine whether jumps are present in asset returns or other discretely sampled processes. As the sampling interval tends to 0, our test statistic converges to 1 if there are jumps, and to another deterministic and known value (such as 2) if there are no jumps. The test is valid for all Itô semimartingales, depends neither on the law of the process nor on the coefficients of the equation which it solves, does not require a preliminary estimation of these coefficients, and when there are jumps the test is applicable whether jumps have finite or infiniteactivity and for an arbitrary Blumenthal–Getoor index. We finally implement the test on simulations and asset returns data.
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.
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 26 (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.
Testing for common arrivals of jumps for discretely observed multidimensional processes
, 2009
"... We consider a bivariate process Xt = (X 1 t,X 2 t), which is observed on a finite time interval [0,T] at discrete times 0,∆n,2∆n,.... Assuming that its two components X¹ and X² have jumps on [0,T], we derive tests to decide whether they have at least one jump occurring at the same time (“common jump ..."
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Cited by 23 (3 self)
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We consider a bivariate process Xt = (X 1 t,X 2 t), which is observed on a finite time interval [0,T] at discrete times 0,∆n,2∆n,.... Assuming that its two components X¹ and X² have jumps on [0,T], we derive tests to decide whether they have at least one jump occurring at the same time (“common jumps”) or not (“disjoint jumps”). There are two different tests for the two possible null hypotheses (common jumps or disjoint jumps). Those tests have a prescribed asymptotic level, as the mesh ∆n goes to 0. We show on some simulations that these tests perform reasonably well even in the finite sample case, and we also put them in use for some exchange rates data.
Detecting Jumps from Lévy JumpDiffusion Processes
 JOURNAL OF FINANCIAL ECONOMICS
, 2009
"... Recent assetpricing models incorporate jump risk through Lévy processes in addition to diffusive risk. This paper studies how to detect stochastic arrivals of small and big Lévy jumps with new nonparametric tests. The tests allow for robust analysis of their separate characteristics and facilitate ..."
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Cited by 16 (0 self)
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Recent assetpricing models incorporate jump risk through Lévy processes in addition to diffusive risk. This paper studies how to detect stochastic arrivals of small and big Lévy jumps with new nonparametric tests. The tests allow for robust analysis of their separate characteristics and facilitate better estimation of return dynamics. Empirical evidence of both small and big jumps based on these tests suggests that models for individual equities and overall market indices require incorporating Lévytype jumps. The evidence of small jumps also helps explain why jumps in the market index are uncorrelated with jumps in its component equities.
jumps, and diversification
 Journal of Econometrics
, 2008
"... We test for price discontinuities, or jumps, in a panel of highfrequency intraday returns for forty largecap stocks and an equiweighted index from these same stocks. Jumps are naturally classified into two types: common and idiosyncratic. Common jumps affect all stocks, albeit to varying degrees, ..."
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Cited by 16 (0 self)
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We test for price discontinuities, or jumps, in a panel of highfrequency intraday returns for forty largecap stocks and an equiweighted index from these same stocks. Jumps are naturally classified into two types: common and idiosyncratic. Common jumps affect all stocks, albeit to varying degrees, while idiosyncratic jumps are stockspecific. Despite the fact that each of the stocks has a β of about unity with respect to the index, common jumps are virtually never detected in the individual stocks. This is truly puzzling, as an index can jump only if one or more of its components jump. To resolve this puzzle, we propose a new test for cojumps. Using this new test we find strong evidence for many modestsized common jumps that simply pass through the standard jump detection statistic, while they appear highly significant in the cross section based on the new cojump identification scheme. Our results are further corroborated by a striking withinday pattern in the nondiversifiable cojumps.
Inference for the Jump Part of Quadratic Variation OF ITO SEMIMARTINGALES
 CREATES RESEARCH PAPER
, 2008
"... ..."
Realized Volatility When Sampling Times are Possibly Endogenous
, 2009
"... When estimating integrated volatilities based on highfrequency data, simplifying assumptions are usually imposed on the relationship between the observation times and the price process. In this paper, we establish a central limit theorem for the Realized Volatility in a general endogenous time sett ..."
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Cited by 9 (1 self)
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When estimating integrated volatilities based on highfrequency data, simplifying assumptions are usually imposed on the relationship between the observation times and the price process. In this paper, we establish a central limit theorem for the Realized Volatility in a general endogenous time setting. We also document that this endogeneity is present in financial data.