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Excerpt from Estimating the Variance Parameter From Noisy High Frequency Financial Data I call the diffusion process the signal process and the fit observation noise. The observation noise is the deviation of data from the continuous process and is assumed to be independent from the diffusion process. Many things contribute to this observation noise. In the currency market, for example, non-binding quoting error is part of the noise. In other markets, bid and offer difference also contributes to the observation noise. Many other micro structural behaviors are all included in this so - called observation noise. For low frequency observations, the observation noise is overwhelmed by the sig nal change. When observation frequency increases, the signal change becomes smaller and smaller while the size of the noise remains the same. The noise totally dominates the price change in ultra-high frequency data. Viewing high frequency data as observation with noise certainly captures many basic characteristics of high frequency financial time series mentioned above. 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.