Abstract:
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This paper presents nonparametric inference for nonlinear volatility functionals of general multivariate Ito semimartingales, in high-frequency and noisy setting. The estimator achieves the optimal convergence rate by local moving averages, jump truncation, spatial localization and high-order nonlinearity bias correction. A stable central limit theorem is attained with estimable asymptotic covariance matrix, and forms a basis for infill asymptotic results of, for example, the realized Laplace transform, the realized principal component analysis, the linear continuous-time regression, and the generalized method of integrated moments, hence helps to extend the application scopes to more frequently sampled noisy data.
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