Inference for Volatility Functionals of Multivariate It\^o Semimartingales Observed with Jump and Noise
Abstract
This paper presents the nonparametric inference for nonlinear volatility functionals of general multivariate It\^o semimartingales, in high-frequency and noisy setting. Pre-averaging and truncation enable simultaneous handling of noise and jumps. Second-order expansion reveals explicit biases and a pathway to bias correction. Estimators based on this framework achieve the optimal convergence rate. A class of stable central limit theorems are attained with estimable asymptotic covariance matrices. This paper form a basis for infill asymptotic results of, for example, the realized Laplace transform, the realized principal component analysis, the continuous-time linear regression, and the generalized method of integrated moments, hence helps to extend the application scopes to more frequently sampled noisy data.
Keywords
Cite
@article{arxiv.1810.04725,
title = {Inference for Volatility Functionals of Multivariate It\^o Semimartingales Observed with Jump and Noise},
author = {Richard Y. Chen},
journal= {arXiv preprint arXiv:1810.04725},
year = {2019}
}