Excerpt from High Frequency Data and Volatility, in Foreign Exchange Rates Exchange rates, like many other financial time series, display substantial heteroscedasticity. This poses obstacles in detecting trends and changes. Understanding volatility becomes extremely important in studying financial time series. Unfortunately, estimating volatility from low frequency data, such as daily, weekly, or monthly observations, is very difficult. The recent availability of ultra-high frequency observations, such as tick-by-tick data, to large financial institutions creates a new possibility for the analysis of volatile time series. This article uses tick-by-tick Deutsche Mark and US Dollar (DM/$) exchange rates to explore this new type of data. Unlike low frequency data, high frequency data have extremely high negative first order autocorrelation in their return. A model explaining the negative autocorrelation and volatility estimators using the high frequency data are proposed. Daily and hourly volatility of the DM/$ exchange rates are estimated and the behaviors of the volatility are discussed. 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.