Filip Stoklasa, Laura Caban, Daniela Majerčáková, Faculty of Mathematics, Physics and Informatics, Comenius University Bratislava, Slovak Republic
Ľudomír Šlahor, Faculty of Management, Comenius University Bratislava, Slovak Republic

Type of article: scientific article
Pages: 45 – 61

Abstract

This paper examines the efficiency, dynamics, and predictability of selected foreign exchange rates through an analysis of the Hurst exponent. The aim of the study is to investigate the presence and intensity of long-term dependence, capture time-varying market regimes, and analyze the relationship between the Hurst exponent and realized volatility for four major currency pairs: EUR/USD, GBP/USD, USD/JPY, and USD/CHF. The study is based on daily logarithmic returns of the selected currency pairs over the period 2005–2026 and assesses the extent to which their behavior is consistent with the Efficient Market Hypothesis. The results of the global R/S (rescaled range) analysis provide no evidence of statistically significant long-term memory in any of the examined currency pairs. However, rolling estimates of the Hurst exponent reveal substantial temporal variation and alternating persistent and anti-persistent regimes. The analysis of the relationship between the Hurst exponent and realized volatility further indicates a predominantly negative association, with higher volatility observed in most cases during anti-persistent regimes. The findings suggest that global estimates of the Hurst exponent may obscure substantial time variation in the dynamics of foreign exchange market, while rolling estimates provide additional information about changing market regimes.