Wavelet multiresolution analysis of high-frequency Asian FX rates, Summer 1997

Foreign exchange (FX) pricing processes are nonstationary: Their frequency characteristics are time dependent. Most do not conform to Geometric Brownian Motion (GBM), because they exhibit a scaling law with Hurst exponents between zero and 0.5 and fractal dimensions between 1.5 and 2. Wavelet multiresolution analysis (MRA), with Haar wavelets, is used to analyze these time and scale dependencies (self-similarity) of intraday Asian currency spot exchange rates. We use the ask and bid quotes of the currencies of eight Asian countries (Japan, Hong Kong, Indonesia, Malaysia, Philippines, Singapore, Taiwan, and Thailand) and, for comparison, of Germany for the crisis period May 1, 1998-August 31, 1997, provided by Telerate (U.S. dollar is the numéraire). Their time-scale-dependent spectra, which are localized in time, are observed in wavelet scalograms. The FX increments are characterized by the irregularity of their singularities. Their degrees of irregularity are measured by homogeneous Hurst exponents. These critical exponents are used to identify the global fractal dimension, relative stability, and long-term dependence, or long-term memory, of each Asian FX series. The invariance of each identified Hurst exponent is tested by comparing it at varying time and scale (frequency) resolutions. It appears that almost all investigated FX markets show antipersistent pricing behavior. The anchor currencies of the D-mark and Japanese Yen (JPY) are ultraefficient in the sense of being most antipersistent or “fast mean-reversing.” This is a surprising result because most financial analyst either assume neutral or persistent behavior in the financial markets, based on earlier research by Granger in the 1960s. This is a pedagogical paper explaining the most rational methodology for the identification of long-term memory in financial time series.