Conventional time series analysis, focusing exclusively on a time series at a given scale, lacks the ability to explain the nature of the data generating process. A process equation that successfully explains daily price changes, for example, is unable to characterize the nature of hourly price...

This paper presents an empirical investigation of scaling and multifractal properties of U.S. Dollar-Deutschemark (USD-DEM) returns. The data set is ten years of 5-minute returns. The cumulative return distributions of positive and negative tails at di.erent time intervals are linear in the...