Large Deviations of the Threshold Estimator of Integrated (Co-)Volatility Vector in the Presence of Jumps

Recently considerable interest has been paid to the estimation problem of the realized volatility and covolatility by using high-frequency data of financial price processes in financial econometrics. Threshold estimation is one of the useful techniques in the inference for jump-type stochastic processes from discrete observations. In this paper, we adopt the threshold estimator introduced by Mancini (Scand Actuar J 1:42–52, 2004) where only the variations under a given threshold function are taken into account. The purpose of this work is to investigate large and moderate deviations for the threshold estimator of the integrated variance–covariance vector. This paper is an extension of the previous work in Djellout et al. (Stoch Process Appl 1–35, 2017), where the problem has been studied in the absence of a jump component. We will use the approximation lemma to prove large and moderate deviations results. As the reader can expect, we obtain the same results as in the case without jump.