This paper presents the nonparametric inference for nonlinear volatility functionals of general multivariate It\^o semimartingales, in high-frequency and noisy setting. The estimator achieves the optimal convergence rate after explicit bias correction. A stable central limit theorem is attained with estimable asymptotic covariance matrix .
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 .
R
The estimator achieves
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
R
after explicit bias correction. A
. A class of
R
theorem is
theorems are
R
matrix
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