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71
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 infinite-activity 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 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.
Testing for common arrivals of jumps for discretely observed multidimensional processes. Unpublished working paper
, 2007
"... Abstract We consider a bivariate process X t = (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 X 1 and X 2 have jumps on [0, T ], we derive tests to decide whether they have at least one jump occurring ..."
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Cited by 23 (3 self)
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Abstract We consider a bivariate process X t = (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 X 1 and X 2 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 Jump-Diffusion Processes
- JOURNAL OF FINANCIAL ECONOMICS
, 2009
"... Recent asset-pricing 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 asset-pricing 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 Lévy-type jumps. The evidence of small jumps also helps explain why jumps in the market index are uncorrelated with jumps in its component equities.
Inference for the Jump Part of Quadratic Variation OF ITO SEMIMARTINGALES
- CREATES RESEARCH PAPER
, 2008
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jumps, and diversification
- Journal of Econometrics
, 2008
"... We test for price discontinuities, or jumps, in a panel of high-frequency intraday returns for forty large-cap 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 high-frequency intraday returns for forty large-cap 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 stock-specific. 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 modest-sized 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 within-day pattern in the non-diversifiable cojumps.
Jumps, cojumps and macro announcements.
- Journal of Applied Econometrics
, 2011
"... Abstract We use recently proposed tests to extract jumps and cojumps from three types of assets: stock index futures, bond futures, and exchange rates. We then characterize the dynamics of these discontinuities and informally relate them to U.S. macroeconomic releases before using limited dependent ..."
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Cited by 15 (1 self)
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Abstract We use recently proposed tests to extract jumps and cojumps from three types of assets: stock index futures, bond futures, and exchange rates. We then characterize the dynamics of these discontinuities and informally relate them to U.S. macroeconomic releases before using limited dependent variable models to formally model how news surprises explain (co)jumps. Nonfarm payroll and federal funds target announcements are the most important news across asset classes. Trade balance shocks are important for foreign exchange jumps. We relate the size, frequency and timing of jumps across asset classes to the likely sources of shocks and the relation of asset prices to fundamentals in the respective classes.
