Long-memory of foreign exchange rate data

Abstract

This paper investigates long-memory of foreign exchange rate data by the fractional Brownian motion (fBm). We use the principle of spectral density function to find the range of Hurst parameter (H) of the fBm. If 0< H <1/2, then it has a short-range dependence (SRD). It simulates long-range dependence (LRD) if 1/2< H <1. The curve of foreign exchange rate data is fBm because of the specific appearance of the Hurst parameter (H). Our results indicate that there exists a long-range dependence (LRD) or a long- memory for the foreign exchange rate data. If it has LRD, then it has memory predictable in Time Series method for the next step.