Testing for Jumps in a Discretely Observed Process

By Yacine Aït-Sahalia, Jean Jacod. 2009

598 citations recorded by the source corpus.

We propose a new test to determine whether jumps are present in asset returns or other discretelly sampled processses. 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 Ito 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.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/59991111a6d82a0422edcedcb973fc038a4ff1a7

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Citations in the corpus

Modeling financial contagion using mutually exciting jump processes (2015, unknown): “…and Mykland (2008) and Lee and Hannig (2010)), bipower variations (Barndorff-Nielsen and Shephard (2006) and Huang and Tauchen (2005)), power variations (Äıt-Sahalia and Jacod (2009) and Fan and Fan (2011)), truncation methods (Corsi et al. (2010)), evidence from options returns regarding…”
Jumps and Betas: A New Framework for Disentangling and Estimating Systematic Risks (2010, unknown): “Ait-Sahalia and Jacod (2008a) of the process p0 on [0;T].”
Estimation of continuous-time stochastic volatility models with jumps using high-frequency data (2009, background): “Numerous non-parametric tests have been proposed for the presence of jumps on the “observed” path of increasingly finer-sampled processes, see Ait-Sahalia and Jacod (2008b), Barndorff-Nielsen and Shephard (2004, 2006a), Huang and Tauchen (2005), Jiang and Oomen (2005), Lee and Mykland (2007),…”
Analyzing the Spectrum of Asset Returns: Jump and Volatility Components in High Frequency Data (2010, methodology): “…to finite or infinite variation for X, and Todorov and Tauchen (2010), who provide a graphical method to determine whether β = 2 or β 2 using the test statistic of Aït-Sahalia and Jacod (2009b), and Belomestny (2010) who proposes a method based on low frequency historical and options data.”
Nonparametric tests for pathwise properties of semimartingales (2011, methodology): “ich class of models – diﬀusion, jump-diﬀusion or pure-jump – is the most appropriate for a given data set. Nonparametric procedures have been recently proposed for investigating the presence of jumps [2, 6, 17] and studying some ﬁne properties of the jumps [3, 4, 25, 26] This is an electronic reprin”
IDENTIFYING THE BROWNIAN COVARIATION FROM THE CO-JUMPS GIVEN DISCRETE OBSERVATIONS (2012, methodology): “…to show that, for finite samples, the log version of the bipower variation has a better performance than bipower variation; or in the same spirit as Aı̈t-Sahalia and Jacod (2009b), who use simulations to choose the threshold parameters α and as well as the parameters k, p, and kn involved in their…”
Estimation of integrated volatility of volatility with applications to goodness-of-fit testing (2011, background): “whether there are jumps or not in the process, whether there are finitely or infinitely many, or what in general their degree of activity is (see foremost [1]–[3], but also [7] or [26]).”
HAR Modeling for Realized Volatility Forecasting (2012, unknown): “Recent research focusing on jump detection and volatility measuring in presence of jumps includes [12], [62], [59], [56], [2], [1], [29], [63] and [24].”
Cross-Stock Comparisons of the Relative Contribution of Jumps to Total Price Variance (2012, background): “Some of these techniques exploit properties of the higher-order moments of the price process, which will have different behavior depending on whether a jump is present (Ait-Sahalia & Jacod, 2009; Jiang & Oomen, 2008).”
Activity Signature Functions for High-Frequency Data Analysis (2010, methodology): “We first compute for an arbitrary interval of time the realized power variation over two different time scales, a strategy derived from Ait-Sahalia and Jacod (2009a) and Ait-Sahalia and Jacod (2009b) (see also Zhang et al. (2005)).”