Multifractal Features in the Foreign Exchange and Stock Markets

TL;DR

This paper investigates the multifractal properties of tick data in the Korean financial market, revealing persistent long-memory effects and specific distribution characteristics of returns.

Contribution

It applies rescaled range analysis to Korean market data, demonstrating multifractality, long-term memory, and the distribution of returns, which are novel insights for this market.

Findings

Market exhibits multifractal behavior and long-term memory effects.

Hurst exponents show crossovers at characteristic time scales.

Return distributions align with Lorentz distribution, not fat-tailed.

Abstract

The multifractal behavior for tick data of prices is investigated in Korean financial market. Using the rescaled range analysis(R/S analysis), we show the multifractal nature of returns for the won-dollar exchange rate and the KOSPI. We also estimate the Hurst exponent and the generalized $q$th-order Hurst exponent in the unversal multifractal framework. Particularly, our financial market is a persistent process with long-run memory effects, and the statistical value of the Hurst exponents occurs the crossovers at charateristic time scales. It is found that the probability distribution of returns is well consistent with a Lorentz distribution, significantly different from fat-tailed properties.