Analysis of Indian Foreign Exchange Markets: A Multifractal Detrended Fluctuation Analysis (MFDFA) Approach

Abstract

The objectives of this paper are to analyse the presence of multifractality in daily exchange rates of the US dollar (USD), British Pound (GBP), Euro (EUR), and Japanese Yen (JPY) relative to the Indian Rupee (INR) for a specific period (1999–2018) and to investigate the source of the observed multifractality in these exchange rates. The research examines the multifractal spectra of logarithmic returns (daily price changes) for the four currencies. To investigate the origins of this multifractality, we conduct two transformations on the return series: (a) random shuffling of the original time series of logarithmic returns which disrupts any long-range correlations within the data. And (b) application of phase randomisation on the unaltered series which aims to preserve frequency information while altering timing-related characteristics of the data. We then look at the impact of these transformations on the multifractality. Our findings indicate that all four exchange rates exhibit multifractal characteristics in their return series. The source of multifractality differs between currencies: The USD is primarily driven by the “fat tail” of the distribution (extreme fluctuations). For the GBP and EUR, a combination of long-range correlations and fat tails contributed to multifractality. The JPY is mainly influenced by the broad tail of the distribution (more frequent but smaller fluctuations). These results have implications for policymakers and market participants. Based on these findings, policymakers should consider the specific characteristics of each currency when designing risk management strategies or regulatory interventions.

Keywords

• Multifractal
• exchange rates
• fluctuation analysis
• long-range correlation
• fat-tailed distributions