Multifractal Measures for the Yen-Dollar Exchange Rate

TL;DR

This paper analyzes the multifractal properties of the yen-dollar exchange rate using rescaled range analysis, revealing crossover behavior in Hurst exponents and Lorentz distribution characteristics in the rate's probability distribution.

Contribution

It introduces the application of multifractal analysis to the yen-dollar exchange rate and identifies unique crossover phenomena and distribution forms.

Findings

Existence of a crossover in Hurst exponents at specific time scales.

The exchange rate's distribution follows a Lorentz distribution, not fat-tailed.

Differences in multifractal behavior between exchange rate and bond futures.

Abstract

We study the tick dynamical behavior of the yen-dollar exchange rate using the rescaled range analysis in financial market. It is found that the multifractal Hurst exponents with the short and long-run memory effects can be obtained from the yen-dollar exchange rate. This exists one crossover for the Hurst exponents at charateristic time scales, while the bond futures exists no crossover. Particularly, it is shown that the probability distribution of the yen-dollar exchange rate has one form of the Lorentz distribution rather than fat-tailed properties, which is similar to that of for the won-dollar exchange rate.