Evolution of Scaling Behaviors in Currency Exchange Rate Series

Abstract

Scaling invariance in exchange rate series can shed light on the nonefficiency of foreign exchange markets and be used subsequently in prediction. Extensive works have been done to evaluate scaling exponents from exchange rate series with lengths covering several decades or more, during which great changes may have occurred in society, economics, and finance. A natural question is whether the scaling invariance exists in every short time period, and how it evolves? In this paper, the correlation-corrected balanced estimation of diffusion entropy (cBEDE) is used to evaluate local scaling behavior embedded in exchange rate series and its evolution. A total of six exchanges between the most important currencies in about 20 years are investigated. It is found that all the three-year segments behave scale-invariant. The evolution of the scaling behavior displays rich patterns at different time scales. Especially, in the periods corresponding to the famous events in the global financial system, the scaling behavior has distinct patterns such as a monotonic increase or decrease, a valley, or a peak. We hope our work can stimulate much more works on evolutionary processes of financial systems.

Cellular coupling determines scale-invariant behavior of neurons in suprachiasmatic nucleus

“…In this section, we introduce the definition of the scale-invariance, and how to de-trend the data, the method of Diffusion Entropy, and the methods of Diffusion Entropy Analysis (DEA) and cBEDE, which are developed from the method of Diffusion Entropy. The details for the method of Diffusion Entropy, DEA, and cBEDE can be found elsewhere (Feng et al 2019;Grigolini et al 2001;Pan et al 2014aPan et al , 2014bQi and Yang 2011;Zhang et al 2012).…”

“…Accordingly, the cBEDE method can simultaneously reduce the bias and variance of estimation of diffusion entropy, and is presented elsewhere (Feng et al 2019;Grigolini et al 2001;Pan et al 2014aPan et al , 2014bQi and Yang 2011;Zhang et al 2012). Briefly, the cBEDE method can estimate the entropy, and derive a reliable scaling exponent δ for short time series with a length of only several hundred data points, and is characterized by the following equation:…”