Testing for Common Arrivals of Jumps for Discretely Observed Multidimensional Processes

By Jean Jacod, V. Todorov. 2009

172 citations recorded by the source corpus.

We consider a bivariate process Xt = (X 1 t ;X 2 t ), which is observed on a flnite 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 difierent 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 flnite sample case, and we also put them in use for some exchange rates data.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/0e225bf1fefe0ed8238e4879ddd886746f19a90f

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Citations in the corpus

INFERENCE FOR THE JUMP PART OF QUADRATIC VARIATION OF ITÔ SEMIMARTINGALES (2009, background): “Very recent work by Barndorff-Nielsen & Shephard (2007a) and Jacod & Todorov (2007) has already addressed the question of testing for common and disjoint jumps of multivariate price processes.”
Systemic Co-Jumps (2017, unknown): “Jacod and Todorov (2009) propose two tests for co-jumps, building on functionals that depend, asymptotically, on co-jumps only.”
Testing for Jumps When Asset Prices are Observed with Noise - A Swap Variance Approach (2008, unknown): “Niederhoffer and Osborne (1966) is one of the first studies to recognize that the existence of a bid-ask spread leads to a negative first order serial correlation in observed returns (see also Roll, 1984).”
Risk, Jumps, and Diversification (2008, result): “Although these specific numbers obviously rely on our use of the popular BN-S procedure for identifying jumps, the same basic findings of more frequent and larger sized jumps for the individual stocks compared to the index is entirely consistent with the limited empirical evidence based on the univa”
IDENTIFYING THE BROWNIAN COVARIATION FROM THE CO-JUMPS GIVEN DISCRETE OBSERVATIONS (2012, methodology): “In the presence of (possibly infinite activity) jumps in a bivariate model, in Jacod and Todorov (2009), B̂n := ∑nj=1( j X (1))2( j X (2))2 is used to estimate B := ∑s≤T ( X (1)s )2( X (2)s )2: B̂n is not directly comparable (as for the efficiency) with the estimate of the sum of the co-jumps ∑s≤T…”
Is the diurnal pattern sufficient to explain intraday variation in volatility? A nonparametric assessment (2017, unknown): “Note that ˇΣ n is related to recent work on asymptotic variance estimation by Mykland and Zhang (2017); see also, e.g., Christensen, Podolskij, Thamrongrat, and Veliyev (2017); Jacod and Todorov (2009); Mancini and Gobbi (2012).”
Bipower Variation for Gaussian Processes with Stationary Increments (2009, unknown): “also [5]), and applications to finance of such extensions are discussed in [20] and [28].”
Limit Theorems for Power Variations of Pure-Jump Processes with Application to Activity Estimation (2011, background): “Recently, Ait-Sahalia and Jacod (2009b) have used the realized power variation as a way to test for presence of jumps on a given path and Jacod and Todorov (2009) have used it to test for common arrival of jumps in a multivariate context.”
Variance Risk-Premium Dynamics: The Role of Jumps (2010, methodology): “Further, I compute the share in the cojump variation measure of Jacod and Todorov (2009) due to negative jumps in the returns and positive jumps in the volatility (which arrive at the same time).”
Jumps and Betas: A New Framework for Disentangling and Estimating Systematic Risks (2010, unknown): “we build on some of the results in Jacod and Todorov (2008) .”
Econometrics of co-jumps in high-frequency data with noise (2015, methodology): “Our notation follows Jacod (2012) and Jacod and Todorov (2009), among others, and we refer to Jacod (2012) for background information on semimartingales.”
Outlyingness weighted covariation (2011, unknown): “The constant c is usually calibrated at a multiple (often 9) of a first step estimate of the daily volatility (Äıt-Sahalia and Jacod, 2009), such as the realized bipower variation (Jacod and Todorov, 2009) or the GARCH volatility prediction (Mancini and Renó, 2011).”
Do price and volatility jump together (2010, methodology): “4 of [6] to obtain that, if Zn P −→ Z are F-measurable variables, we have P̃(U(n, 1) > Zn | F) P −→ P̃(UT > Z | F).”
Resolution of Policy Uncertainty and Sudden Declines in Volatility (2017, unknown): “9 There is a large literature on jump detection with intraday data, see e.g. Huang and Tauchen (2005), Barndorff-Nielsen and Shephard (2006), Lee and Mykland (2008), Jiang and Oomen (2008), Jacod and Todorov (2009), and Aït-Sahalia and Jacod (2009).”