Authors: Dr. CHARU BHURAT¹, PRATIK T. RUPAREL², SANJEET GHATPANDE³ and KALP PANDYA⁴

Abstract

This study explores long-term memory in Indian forex markets by analysing daily exchange rate returns for USD/INR, EUR/INR, GBP/INR and JPY/INR from 2000 to 2024. We evaluate the mean and volatility dynamics of these currency pairs using a variety of fractal models, including ARFIMA, FIGARCH, and APARCHFIGARCH techniques. Stationarity tests suggest that all series are stationary, whereas Hurst exponent analysis shows persistent behaviour (H > 0.5) for USD/INR and JPY/INR, as well as near-random walk behaviour for EUR/INR and GBP/INR. The ARFIMA estimation for the mean gives no significant long-memory impact (d = 0) for certain pairs, while the FIGARCH and APARCH-FIGARCH models captured strong long-term persistence and asymmetric volatility. These findings imply that, while the efficient market theory holds that exchange rates follow a random walk, the presence of long memory, particularly in volatility, implying that the Fractal Market Hypothesis holds in the Indian Forex Markets. The findings reveal persistent and asymmetric volatility in INR currency pairs, aiding traders in refining hedging, VaR estimation, and option pricing models. For central banks, this suggests the need for timely and sustained interventions to ensure exchange rate stability.

Keywords: Indian Forex Markets, Fractional Integration, ARFIMA, ARMA, FIGARCH, FIAPARCH.

Download PDF