Title: Estimation of the quadratic variation and its eigenvalues for multivariate jump processes
Authors: Mark Podolskij - Aarhus University (Denmark) [presenting]
Abstract: New asymptotic theory for the estimation of quadratic variation in the setting of multivariate jump processes is presented. In financial applications quadratic variation plays a key role in the assessment of risk. In the past decade there have been numerous studies on statistical inference for quadratic variation. The mathematical theory depends very much on the particular modelling framework: when the jump part is absent the statistical theory is well understood since the 90's; if the Brownian and the jump parts are present the weak limit results, which have been investigated previously, are quite non-standard. We will consider the setting when the underlying semimartingale is a multivariate pure jump process. We will investigate the weak limit theory for the matrix-valued quadratic variation, present the corresponding results for its random eigenvalues and discuss how the theory can be applied in practice.