Asymptotic efficiency for covariance estimation under noise and asynchronicity

09/07/2018

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by   Sebastian Holtz, et al.

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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 for a fundamental parametric model give rise to infinite-dimensional convolution theorems for covariation estimation under asynchronicity, which is an essential estimation problem in finance. A main tool marks the verification of asymptotic Le Cam equivalence between general discrete and continuous Gaussian experiments, which itself is a result of independent interest.