Asymptotic efficiency for covariance estimation under noise and asynchronicity

Abstract

The estimation of the covariance structure from a discretely observed multivariate Gaussian process under asynchronicity and noise is analysed under high-frequency asymptotics. Asymptotic lower and upper bounds are established for a general Gaussian framework which provides benchmark cases for various Gaussian process models of interest. The parametric bounds give rise to infinite-dimensional convolution theorems for covariation estimation under asynchronicity, which is an essential estimation problem in finance.

References in corpus (5)

• On covariation estimation for multivariate continuous Itô semimartingales with noise in non-synchronous observation schemes
• Asymptotic Equivalence for Nonparametric Regression
• Functional stable limit theorems for quasi-efficient spectral covolatility estimators
• Le cam theory on the comparison of statistical models
• Exact spectral asymptotics of fractional processes