Long memory in high frequency foreign exchange rates: Hurst exponents dependence on data aggregation

Abstract

This paper presents the study on long memory in absolute daily returns of the US dollar versus euro, the British pound and the Japanese yen aggregated foreign exchange rates. Pointwise, maximum price, minimum price and average price aggregation rules for high frequency foreign exchange rates are introduced. The classical R/S statistic is used to analyze Hurst exponents dependence on the choice of data aggregation function.