Wavelet Based Volatility Clustering Estimation of Foreign Exchange Rates

TL;DR

This paper introduces a wavelet-based method to detect volatility clustering and chaos in foreign exchange rate time series, revealing nonlinearity in some currencies but not in others due to government control.

Contribution

The study applies continuous wavelet transform analysis to identify intermittencies and chaos in FX data, providing a novel approach in financial time series analysis.

Findings

Chaos observed in US/EUR and US/UK exchange rates.

No chaos detected in US/INR exchange rates.

Wavelet analysis effectively detects nonlinearity and intermittencies.

Abstract

We have presented a novel technique of detecting intermittencies in a financial time series of the foreign exchange rate data of U.S.- Euro dollar(US/EUR) using a combination of both statistical and spectral techniques. This has been possible due to Continuous Wavelet Transform (CWT) analysis which has been popularly applied to fluctuating data in various fields science and engineering and is also being tried out in finance and economics. We have been able to qualitatively identify the presence of nonlinearity and chaos in the time series of the foreign exchange rates for US/EURO (United States dollar to Euro Dollar) and US/UK (United States dollar to United Kingdom Pound) currencies. Interestingly we find that for the US-INDIA(United States dollar to Indian Rupee) foreign exchange rates, no such chaotic dynamics is observed. This could be a result of the government control over the foreign exchange rates, instead of the market controlling them.