This paper studies the stationary bootstrap applicability for realized covariations of high frequency asynchronous financial data. The stationary bootstrap method, which is characterized by a block-bootstrap with random block length, is applied to estimate the integrated covariations. The bootstrap realized covariance, bootstrap realized regression coefficient and bootstrap realized correlation coefficient are proposed, and the validity of the stationary bootstrapping for them is established both for large sample and for finite sample. Consistencies of bootstrap distributions are established, which provide us valid stationary bootstrap confidence intervals. The bootstrap confidence intervals do not require a consistent estimator of a nuisance parameter arising from nonsynchronous unequally spaced sampling while those based on a normal asymptotic theory require a consistent estimator. A Monte-Carlo comparison reveals that the proposed stationary bootstrap confidence intervals have better coverage probabilities than those based on normal approximation.
Bibliographical noteFunding Information:
This work was supported by the National Research Foundation of Korea (NRF-2016R1A2B4008780, NRF-2015-1006133 and NRF-2012-2046157) through the National Research Foundation of Korea (NRF) funded by the Ministry of Education Science and Technology.
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- Stationary bootstrap
- realized correlation coefficient
- realized covariance
- realized regression coefficient