Scaling, Self-Similarity and Multifractality in FX Markets

Physica A, 323, pp. 578 – 590, 2003

13 Pages Posted: 4 May 2012

See all articles by Zhaoxia Xu

Zhaoxia Xu

UNSW Australia Business School, School of Banking and Finance

Ramazan Gencay

Simon Fraser University

Date Written: November 14, 2002

Abstract

This paper presents an empirical investigation of scaling and multifractal properties of US Dollar–Deutschemark (USD–DEM) returns. The data set is ten years of 5-min returns. The cumulative return distributions of positive and negative tails at different time intervals are linear in the double logarithmic space. This presents strong evidence that the USD–DEM returns exhibit power-law scalingin the tails. To test the multifractal properties of USD–DEM returns, the mean moment of the absolute returns as a function of time intervals is plotted for different powers of absolute returns. These moments show different slopes for these powers of absolute returns. The nonlinearity of the scalingexponent indicates that the returns are multifractal.

Keywords: Scaling, Self-similarity, Multifractality, High-frequency data, Foreign exchange markets

JEL Classification: G0, G1, C1

Suggested Citation

Xu, Zhaoxia and Gencay, Ramazan, Scaling, Self-Similarity and Multifractality in FX Markets (November 14, 2002). Physica A, 323, pp. 578 – 590, 2003, Available at SSRN: https://ssrn.com/abstract=2050566

Zhaoxia Xu (Contact Author)

UNSW Australia Business School, School of Banking and Finance ( email )

Sydney, NSW 2052
Australia

Ramazan Gencay

Simon Fraser University ( email )

Department of Economics
8888 University Drive
Burnaby, British Columbia V5A 1S6
Canada

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