Estimating the Variance Parameter From Noisy High Frequency Financial Data (Classic Reprint)

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Excerpt from Estimating the Variance Parameter From Noisy High Frequency Financial Data Many financial data are now collected at an ultra-high frequency, such as tick-by-tick. However, increasing the observation frequency while keeping the time span of the observation fixed does not always help in estimating parameters. A different type of consistency, the consistency of a estimator as the observation frequency goes to infinity, becomes important in studying high frequency data. In addition to the consistency, the deviation of a financial time series from a continuous process is also increasingly significant as the observation frequency increases. This deviation is not negligible and causes another difficulty in estimating parameters. This paper concentrates on constructing estimators of variance parameter using contaminated observations, i.e., observations from a continuous process with deviation at time of observation. The consistencies of these estimators, as the observation frequency goes to infinity, are analyzed. Key Words: f-consistency, observation noise, quadratic estimator. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully, any imperfections that remain are intentionally left to preserve the state of such historical works.