Topic: Contributed on Monitoring and tracking dependence Title: Testing for Cojumps: A multivariate coexceedance-based approach Authors:  Hans Manner - University of Cologne (Germany) [presenting]
Markus Koesler - University of Cologne (Germany)
Abstract: We consider the problem of testing the synchronicity of jumps, i.e., the presence of cojumps, using high frequency financial data. This is done in the framework of multivariate log price processes with stochastic volatility and compound Poisson jump processes. Testing for cojumps requires a univariate jump detection procedure that tests for and locates jumps. To this end we apply an approach that relies on univariate returns standardized by a jump-robust local volatility estimator. We propose several test statistics for the null hypothesis of independent jump processes against the alternative of dependent jump processes. The test statistics compare the number of coexceedances with their expected number under the null of independent jump processes. We derive the asymptotic distributions of these test statistics under double asymptotics, increasing both the observation frequency and the length of the sample. For finite samples we suggest a block bootstrap procedure that can mitigate size distortions of some of the test statistics. Furthermore, we extend the tests to the context of non-homogeneous jump occurrences using Hawkes processes to model the jump intensities. A comprehensive Monte Carlo study examines the finite sample properties of the tests in a realistic market scenario and an application to financial high-frequency data illustrates its practical use.