Statistical Inference of Spot Correlation and Spot Market Beta under Infinite Variation Jumps[High Frequency Covariance Estimates with Noisy and Asynchronous Data]

Empirical evidence has revealed that the jumps in financial markets appear to be very frequent. This study considers the statistical inference of the spot correlation and the spot market beta between two different assets using high-frequency data, in a setting where both the cojumps and the individual jumps in the underlying driving processes could be of infinite variation. Starting from the estimation of the spot covariance, we propose consistent estimators of the spot correlation and the spot market beta when the jump processes involved are general semimartingales. The second-order approximation for the estimators, namely, the central limit theorems, is established under the assumption that the jumps around zero are of stable Lévy type. Our estimation procedure is based on the empirical characteristic function of the increments of the processes and the application of the polarization identity; the bias terms stemming from the jumps are removed iteratively. The finite sample performances of the proposed estimators and other existing estimators are assessed and compared by using datasets simulated from various models. Our estimators are also applied to some real high-frequency financial datasets.