Large deviations of the Threshold estimator of integrated (co-)volatility vector in the presence of jumps

TL;DR

This paper investigates the large deviations behavior of the threshold estimator for integrated (co-)volatility in financial data, extending previous work to include jump components and confirming similar large deviation principles as in jump-free cases.

Contribution

It extends the analysis of the threshold estimator's large deviations to models with jumps, using approximation techniques to establish the LDP.

Findings

Large deviation principles are established for the threshold estimator with jumps.

Results match those of the jump-free case, indicating robustness of the estimator.

The approach confirms the effectiveness of the threshold method in jump-inclusive models.

Abstract

Recently a considerable interest has been paid on 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 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. where the problem has been studied in absence of the jump component. We will use the approximation lemma to prove the LDP. As the reader can expect we obtain the same results as in the case without jump.