Long range dependence is widespread in nature and has been extensively documented in economics and finance, as well as in hydrology, meteorology, and geophysics by authors such as Heyman, Tabatabai and Lakshman (1991), Hurst (1951), Jones and Briffa (1992), Leland, Taqqu, Willinger and Wilson (1993) and Peters (1994). It has a long history in economics and finance, and has remained a topic of active research in the study of financial time series, Beran (1994).
Historical records of financial data typically exhibit distinct nonperiodical cyclical patterns that are indicative of the presence of significant power at low frequencies (i.e. long range dependencies). However, the statistical investigations that have been performed to test for the presence of long range dependence in economic time series representing returns of common stocks have often become sources of major controversies. Asset returns exhibiting long range dependencies are inconsistent with the efficient market hypothesis, and cause havoc on stochastic analysis techniques that have formed the basis of a broad part of modern finance theory and its applications, Lo (1991). In this chapter, we examine the methods used in Hurst analysis, present a process exhibiting long memory features, and give market evidence by applying Hurst's R/S analysis and finally sketch a trading strategy for German voting and non-voting stocks.