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## Identifying Jumps in Financial Assets: a Comparison between Nonparametric Jump Tests [Extended Version] *

### Citations

1209 |
Statistical methods for research workers
- Fisher
- 1932
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Citation Context ... considered only i.i.d. microstructure noise, in line with most of the papers that introduced these tests to the literature. However, it would be of great interest to observe the impact of zero returns on the behaviour of all these procedures. Second, following the existing literature, in this paper we only considered processes with a finite number of jumps. Thus, a natural extension is a simulation exercise with an infinite number of jumps. Finally, to reduce the probability of detecting spurious jumps, the combination of tests could be enriched by considering test averaging procedures using Fisher (1925)’s method of combining p-values of different tests. We leave these extensions to future research. 38 Procedure Size Power Noise AJ (threshold) slightly undersized; high power at high frequencies which extremely oversized at very high size decreases at lower frequencies diminishes abruptly at lower frequencies frequencies, followed by drastic decreases in size from 1 min onward; very high power which decreases abruptly AJ (power var) oversized; size rapidly high power at high frequencies which extremely oversized at very high increases across the frequency diminishes abruptly at lower frequenci... |

709 | Transform analysis and asset pricing for affine jump-diffusions
- Duffie, Pan, et al.
- 2000
(Show Context)
Citation Context ...tic volatility component, which accommodates the persistence in volatility, and of a jump component, which takes care of the unpredictable, large movements in the price process. The identification of the time and the size of jumps has profound implications in risk management, portfolio allocation, derivatives pricing (Aıt-Sahalia, 2004). For this task, the use of jump diffusion models proved very difficult, as there are no closed forms of the likelihood function and in addition, the number of parameters to estimate is very high. One solution is to focus on the popular class of affine models (Duffie et al., 2000) which allow for tractable estimation, but impose a quite restrictive set of assumptions. An alternative approach is represented by nonlinear volatility models. However, the estimation procedure, based on simulation methods, such as the Gallant and Tauchen (2002)’s efficient method of moments, is computationally demanding and too much dependent on the choice of an auxiliary model (Chernov et al., 2003; Andersen et al., 2002, see, for instance). One of the main advances in high frequency econometrics over the last decade was the development of nonparametric procedures to test for the presence o... |

553 | Answering the skeptics: yes, standard volatility models do provide accurate forecasts
- Andersen, Bollerslev
- 1998
(Show Context)
Citation Context ...ized by persistence, whereas jumps, apart from a possible drift, have an unpredictable nature. The recent literature in the field of high frequency econometrics has developed several estimators for both the quadratic variance and the integrated volatility of a price process such as the one derived in (1). Most of these estimators are based on equally spaced data. Thus, the interval [0, t] is split 3 into n equal subintervals of length δ. The j-th intraday return rj on day t is defined as follows: rj = pt−1+jδ − pt−1+(j−1)δ. (3) [p]t can be estimated by the realized variance (RVt), defined as (Andersen and Bollerslev, 1998): RVt = n∑ j=1 r2j δ→0−→ [p]t, (4) where δ→0−→ stands for convergence in probability when δ → 0. To measure the IV one can use a wide range of estimators, such as multipower variations, threshold estimators, medium and minimum realized variance. All these quantities are robust to jumps in the limit. Most of the jump detection procedures are based on the comparison between RVt, which captures the variation of the process generated by both the diffusion and the jump parts, and a robust to jumps estimator. It is important to note that none of these procedures can test for the absence or presence ... |

326 | 2004b). Power and bipower variation with stochastic volatility and jumps (with discussion
- Barndorff-Nielsen, Shephard
(Show Context)
Citation Context ...his scenario. In the light that the Andersen et al. (2007) and Lee and Mykland (2008) tests differ only in terms of the choice of the critical values, for a large part of our simulation exercise, we do not distinguish between the two of them (see Section 2.2 and the Remarks in Section 3.1). We turn now to the presentation of the procedures. 4 2.1 Barndorff-Nielsen and Shephard (2006) test (BNS henceforth) Barndorff-Nielsen and Shephard (2006) base their procedure on the possibility to build a consistent estimator for the integrated variance of a process. The test draws from previous research (Barndorff-Nielsen and Shephard, 2004), where authors show that the realized bipower variation (BVt) consistently estimates the integrated variance in the presence of rare jumps: BVt = plim δ↓0 n∑ j=2 |rj||rj−1 |(5) Barndorff-Nielsen et al. (2006) generalize the BVt to realized multipower variations, computed as sums of products of adjacent absolute returns raised to certain powers. These quantities can be generally used to estimate ∫ t 0 σms ds, m > 0 in the presence of jumps. One can infer whether jumps occur during a time interval (usually a trading day) by comparing the realized volatility with the realized bipower variation. ... |

169 |
Alternative models for stock price dynamics
- Chernov, Gallant, et al.
- 2003
(Show Context)
Citation Context ...ficult, as there are no closed forms of the likelihood function and in addition, the number of parameters to estimate is very high. One solution is to focus on the popular class of affine models (Duffie et al., 2000) which allow for tractable estimation, but impose a quite restrictive set of assumptions. An alternative approach is represented by nonlinear volatility models. However, the estimation procedure, based on simulation methods, such as the Gallant and Tauchen (2002)’s efficient method of moments, is computationally demanding and too much dependent on the choice of an auxiliary model (Chernov et al., 2003; Andersen et al., 2002, see, for instance). One of the main advances in high frequency econometrics over the last decade was the development of nonparametric procedures to test for the presence of jumps in the path of a price process during a certain time interval or at certain point in time. Such methods are very simple to apply, they just require high frequency transaction prices or mid-quotes. Moreover, they are developed in a model free framework, incorporating different classes of stochastic volatility models. In addition to the seminal contribution of Barndorff-Nielsen and Shephard (200... |

156 | The relative contribution of jumps to total price variation
- Huang, Tauchen
- 2005
(Show Context)
Citation Context ...nsistently estimates the integrated variance in the presence of rare jumps: BVt = plim δ↓0 n∑ j=2 |rj||rj−1 |(5) Barndorff-Nielsen et al. (2006) generalize the BVt to realized multipower variations, computed as sums of products of adjacent absolute returns raised to certain powers. These quantities can be generally used to estimate ∫ t 0 σms ds, m > 0 in the presence of jumps. One can infer whether jumps occur during a time interval (usually a trading day) by comparing the realized volatility with the realized bipower variation. Following simulation studies reported by the authors and also by Huang and Tauchen (2005), in this paper we use the ratio test defined as: 1− BVt RVt√ (µ−41 + 2µ −2 1 − 5)δ max ( 1, TQt BV 2t ) L→ N (0, 1) (6) where µ1 = √ 2/π and L→ stands for convergence in law. TQt represents the realized tripower quarticity that consistently estimates the integrated quarticity, i.e. ∫ t 0 σ4u du, and is defined as follows: TQt = nµ −3 4/3 ( n n− 2 ) n∑ j=3 |rj−2|4/3|rj−1|4/3|rj|4/3 (7) where µ4/3 = E(|U |)4/3, with U being a standard normal variable. 2.2 Andersen et al. (2007) and Lee and Mykland (2008) tests (ABD and LM henceforth) Lee and Mykland (2008) and Andersen et al. (2007) develop tes... |

71 | Jumps in Financial Markets: a New Nonparametric Test and Jump Dynamics,” Review of Financial studies,
- Lee, Mykland
- 2008
(Show Context)
Citation Context ...entre for Econometric Analysis, Faculty of Finance, Cass Business School, 106 Bunhill Row, London EC1Y 8TZ (UK).E-mail Ana.Dumitru.1@city.ac.uk Giovanni URGA Centre for Econometric Analysis, Faculty of Finance, Cass Business School, 106 Bunhill Row, London EC1Y 8TZ (UK). E-mail: g.urga@city.ac.uk & Hyman P. Minsky Department of Economic Studies, University of Bergamo (Italy) Abstract We perform a comprehensive Monte Carlo comparison between nine procedures available in the literature to detect jumps in financial assets proposed by Barndorff-Nielsen and Shephard (2006), Andersen et al. (2007), Lee and Mykland (2008), Aıt-Sahalia and Jacod (2008), Jiang and Oomen (2008), Andersen et al. (2009) (two tests), Corsi et al. (2010) and Podolskij and Ziggel (2010). We evaluate size and power properties of the procedures under alternative sampling frequencies, levels of volatility, persistence in volatility, degree of contamination with microstructure noise, jump size and intensity. The overall best performance is showed by the Lee and Mykland (2008) and Andersen et al. (2007) intraday procedures, provided the price process is not not very volatile. We propose an improvement to these procedures based on critical... |

67 | Testing for jumps in a discretely observed process. - Ait-Sahalia, Jacod - 2009 |

54 | Non-parametric threshold estimation for models with stochastic diffusion coefficient and jumps.
- Mancini
- 2009
(Show Context)
Citation Context ...ersen et al. (2007), Lee and Mykland (2008), Aıt-Sahalia and Jacod (2008), Jiang and Oomen (2008), Andersen et al. (2009) (two tests based on the minimum and median realized variance), Corsi et al. (2010) and Podolskij and Ziggel (2010). All tests are based on CLT-type results that require an intraday sampling frequency that tends to infinity. The test statistics are based on robust to jumps measures of variation in the price processes which are estimated by using one of the following types of estimators: realized multi-power variations (Barndorff-Nielsen et al., 2006), threshold estimators (Mancini, 2009), the median or the minimum realized variation (Andersen et al., 2009), the corrected realized threshold multipower variation (Corsi et al., 2010). The Andersen et al. (2007) and Lee and Mykland (2008) tests have the null hypothesis of continuity of the sample path at a certain moment, allowing for the exact identification of the time of a jump. The other procedures have a null of continuity within a certain time period, such as a trading day. Given such a variety of nonparametric methodologies to identify jumps, one might wonder which 1 procedure should be preferred, or whether there are data... |

51 | Noarbitrage semi-martingale restrictions for continuous-time volatility models subject to leverage effects and jumps: Theory and testable distributional implications
- Andersen, Bollerslev, et al.
- 2006
(Show Context)
Citation Context ...y of Bergamo (Italy) & Centre for Econometric Analysis, Faculty of Finance, Cass Business School, 106 Bunhill Row, London EC1Y 8TZ (UK).E-mail Ana.Dumitru.1@city.ac.uk Giovanni URGA Centre for Econometric Analysis, Faculty of Finance, Cass Business School, 106 Bunhill Row, London EC1Y 8TZ (UK). E-mail: g.urga@city.ac.uk & Hyman P. Minsky Department of Economic Studies, University of Bergamo (Italy) Abstract We perform a comprehensive Monte Carlo comparison between nine procedures available in the literature to detect jumps in financial assets proposed by Barndorff-Nielsen and Shephard (2006), Andersen et al. (2007), Lee and Mykland (2008), Aıt-Sahalia and Jacod (2008), Jiang and Oomen (2008), Andersen et al. (2009) (two tests), Corsi et al. (2010) and Podolskij and Ziggel (2010). We evaluate size and power properties of the procedures under alternative sampling frequencies, levels of volatility, persistence in volatility, degree of contamination with microstructure noise, jump size and intensity. The overall best performance is showed by the Lee and Mykland (2008) and Andersen et al. (2007) intraday procedures, provided the price process is not not very volatile. We propose an improvement to these proc... |

35 | Jump-robust volatility estimation using nearest neighbor truncation. Unpublished paper
- Andersen, Dobrev, et al.
- 2009
(Show Context)
Citation Context ...unhill Row, London EC1Y 8TZ (UK).E-mail Ana.Dumitru.1@city.ac.uk Giovanni URGA Centre for Econometric Analysis, Faculty of Finance, Cass Business School, 106 Bunhill Row, London EC1Y 8TZ (UK). E-mail: g.urga@city.ac.uk & Hyman P. Minsky Department of Economic Studies, University of Bergamo (Italy) Abstract We perform a comprehensive Monte Carlo comparison between nine procedures available in the literature to detect jumps in financial assets proposed by Barndorff-Nielsen and Shephard (2006), Andersen et al. (2007), Lee and Mykland (2008), Aıt-Sahalia and Jacod (2008), Jiang and Oomen (2008), Andersen et al. (2009) (two tests), Corsi et al. (2010) and Podolskij and Ziggel (2010). We evaluate size and power properties of the procedures under alternative sampling frequencies, levels of volatility, persistence in volatility, degree of contamination with microstructure noise, jump size and intensity. The overall best performance is showed by the Lee and Mykland (2008) and Andersen et al. (2007) intraday procedures, provided the price process is not not very volatile. We propose an improvement to these procedures based on critical values obtained from finite sample approximations of the distribution of the t... |

33 |
Testing for Jumps when Asset Prices Are Observed with Noisea “Swap Variance”
- Jiang, Oomen
- 2008
(Show Context)
Citation Context ...s Business School, 106 Bunhill Row, London EC1Y 8TZ (UK).E-mail Ana.Dumitru.1@city.ac.uk Giovanni URGA Centre for Econometric Analysis, Faculty of Finance, Cass Business School, 106 Bunhill Row, London EC1Y 8TZ (UK). E-mail: g.urga@city.ac.uk & Hyman P. Minsky Department of Economic Studies, University of Bergamo (Italy) Abstract We perform a comprehensive Monte Carlo comparison between nine procedures available in the literature to detect jumps in financial assets proposed by Barndorff-Nielsen and Shephard (2006), Andersen et al. (2007), Lee and Mykland (2008), Aıt-Sahalia and Jacod (2008), Jiang and Oomen (2008), Andersen et al. (2009) (two tests), Corsi et al. (2010) and Podolskij and Ziggel (2010). We evaluate size and power properties of the procedures under alternative sampling frequencies, levels of volatility, persistence in volatility, degree of contamination with microstructure noise, jump size and intensity. The overall best performance is showed by the Lee and Mykland (2008) and Andersen et al. (2007) intraday procedures, provided the price process is not not very volatile. We propose an improvement to these procedures based on critical values obtained from finite sample approximations of t... |

27 | Threshold bipower variation and the impact of jumps on volatility forecasting. - Corsi, Pirino, et al. - 2010 |

21 |
Limit Theorems for Multipower Variation
- Barndorff-Nielsen, Shephard, et al.
- 2006
(Show Context)
Citation Context ...his paper we consider eight other tests proposed by Andersen et al. (2007), Lee and Mykland (2008), Aıt-Sahalia and Jacod (2008), Jiang and Oomen (2008), Andersen et al. (2009) (two tests based on the minimum and median realized variance), Corsi et al. (2010) and Podolskij and Ziggel (2010). All tests are based on CLT-type results that require an intraday sampling frequency that tends to infinity. The test statistics are based on robust to jumps measures of variation in the price processes which are estimated by using one of the following types of estimators: realized multi-power variations (Barndorff-Nielsen et al., 2006), threshold estimators (Mancini, 2009), the median or the minimum realized variation (Andersen et al., 2009), the corrected realized threshold multipower variation (Corsi et al., 2010). The Andersen et al. (2007) and Lee and Mykland (2008) tests have the null hypothesis of continuity of the sample path at a certain moment, allowing for the exact identification of the time of a jump. The other procedures have a null of continuity within a certain time period, such as a trading day. Given such a variety of nonparametric methodologies to identify jumps, one might wonder which 1 procedure should b... |

5 | A comprehensive comparison of alternative tests for jumps in asset prices. - Theodosiou, Zikes - 2009 |

2 | Hop, Skip and Jump What Are Modern Jump Tests Finding in Stock Returns?” Working paper,
- Schwert
- 2009
(Show Context)
Citation Context ... reduce the probability of detecting spurious jumps. Finally, we apply the tests to high frequency data for five stocks listed in the New York Stock Exchange, namely Procter&Gamble, IBM, JP Morgan, General Electric and Disney, during 2005 and 2009. To the best of our knowledge, in the literature there are two other papers that deal with similar issues. Theodosiou and Zikes (2010) perform an extensive Monte Carlo simulation exercise to evaluate the performance of different jump detection procedures, with a special interest in the effect of illiquid data on the behaviour of the various tests. Schwert (2009) instead relies only on real data to conclude that different jump detection procedures pick up different jumps. Our paper is more comprehensive in terms of testing procedures included in our comparison. In addition, while we acknowledge that tests for jumps can lead to very different findings, however we provide a feasible solution to this problem first, by proposing the use of simulated critical values for the Andersen et al. (2007) and Lee and Mykland (2008) tests; second, and most importantly, we show that combining various procedures 2 greatly improves the performance of the tests in terms... |

1 | Disentangling Diffusion from - Aıt-Sahalia - 2004 |

1 |
Robust Estimation of Intraweek Periodicity
- Boudt, Croux, et al.
- 2009
(Show Context)
Citation Context ...e case of extremely volatile processes, like the stochastic volatility 36 model with two factors (SV2F), the tests become highly oversized. This is because they standardize each intraday return by a local volatility estimate. When local volatility is very high, the tests will not be able to detect high returns due to jumps. Consequently, their use might not be recommendable for very volatile data. Second, the local volatility of the price process tends to vary a lot during the trading day and exhibits intra-week and intra-day periodicity. The ABD-LM tests do not take into account this factor. Boudt et al. (2009) try to solve this issue by proposing parametric and nonparametric estimators of the periodicity factor that are robust to the presence of jumps. The PZ test displays high power and a very good behavior in the presence of noise, but is also quite oversized. Its size increases very rapidly when the sampling frequency diminishes. However, given its robustness to microstructure effects, it can be successfully applied at high frequencies, without worrying about the noise. The BNS, CPR, Med and Min tests display a similar behaviour. They are all built based on comparisons of the realized variation ... |

1 |
New Tests for Jumps
- Podolskij, Ziggel
- 2010
(Show Context)
Citation Context ...c.uk Giovanni URGA Centre for Econometric Analysis, Faculty of Finance, Cass Business School, 106 Bunhill Row, London EC1Y 8TZ (UK). E-mail: g.urga@city.ac.uk & Hyman P. Minsky Department of Economic Studies, University of Bergamo (Italy) Abstract We perform a comprehensive Monte Carlo comparison between nine procedures available in the literature to detect jumps in financial assets proposed by Barndorff-Nielsen and Shephard (2006), Andersen et al. (2007), Lee and Mykland (2008), Aıt-Sahalia and Jacod (2008), Jiang and Oomen (2008), Andersen et al. (2009) (two tests), Corsi et al. (2010) and Podolskij and Ziggel (2010). We evaluate size and power properties of the procedures under alternative sampling frequencies, levels of volatility, persistence in volatility, degree of contamination with microstructure noise, jump size and intensity. The overall best performance is showed by the Lee and Mykland (2008) and Andersen et al. (2007) intraday procedures, provided the price process is not not very volatile. We propose an improvement to these procedures based on critical values obtained from finite sample approximations of the distribution of the test statistics. We show the validity to use reunion and intersect... |