Analysis of Indian foreign exchange markets: A Multifractal Detrended Fluctuation Analysis (MFDFA) approach

ArXiv ID: 2306.16162 “View on arXiv”

Authors: Unknown

Abstract

The multifractal spectra of daily foreign exchange rates for US dollar (USD), the British Pound (GBP), the Euro (Euro) and the Japanese Yen (Yen) with respect to the Indian Rupee are analysed for the period 6th January 1999 to 24th July 2018. We observe that the time series of logarithmic returns of all the four exchange rates exhibit features of multifractality. Next, we research the source of the observed multifractality. For this, we transform the return series in two ways: a) We randomly shuffle the original time series of logarithmic returns and b) We apply the process of phase randomisation on the unchanged series. Our results indicate in the case of the US dollar the source of multifractality is mainly the fat tail. For the British Pound and the Euro, we see the long-range correlations between the observations and the thick tails of the probability distribution give rise to the observed multifractal features, while in the case of the Japanese Yen, the origin of the multifractal nature of the return series is mostly due to the broad tail.

Keywords: Multifractality, Foreign Exchange, Long-Range Correlations, Fat Tails, Time Series Analysis

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper uses a well-defined, advanced mathematical technique (MFDFA) involving power-law scaling, generalized Hurst exponents, and multifractal spectra to analyze financial data. Empirically, it employs a long-term dataset (20 years), conducts robustness checks (shuffling and phase randomization), and applies the method to specific, real-world exchange rates.

  flowchart TD
    A["Research Goal:<br>Analyze Multifractality in Indian<br>Foreign Exchange Markets"] --> B["Data<br>Exchange Rates (USD, GBP, EUR, JPY vs INR)<br>6 Jan 1999 - 24 Jul 2018"]
    B --> C["Methodology<br>MFDFA on Logarithmic Returns"]
    C --> D{"Detect Multifractality?"}
    D -- Yes --> E["Source Analysis<br>Shuffling vs Phase Randomization"]
    D -- No --> F["No Multifractality Found"]
    E --> G["Key Findings"]
    G --> H["USD: Fat Tails"]
    G --> I["GBP & EUR: Long-Range Correlations + Fat Tails"]
    G --> J["JPY: Broad/Fat Tails"]