Power laws in financial markets: Scaling exponent H and alpha-stable distributions

Abstract

In this study, we analyzed whether daily returns of Brent crude oil, dollar/yen foreign exchange, Dow&Jones Industrial Average Index and 12-month libor display power law features in the scaling exponent and probability distributions or not, using different methods. Due to the fact that the simulated time series with different values showed the robustness of Higuchi's Fractal Dimension and Peng's Statistic, we used these two models in the analysis of the scaling features of the returns. On the other hand, in order to examine power law behaviors of probability distributions, we estimated parameters of the alpha-stable distributions for the return series using the Ecf and Percentile methods. Results showed that the Brent crude oil and 12-month libor have a high persistency in the returns, while the dollar/yen foreign exchange and Dow&Jones Industrial Average Index returns have short memory. According to the alpha-stable parameter estimations, all of the return series have thicker tails than normal distribution. Similar to the highest persistency of 12-month libor returns in the scaling exponent analysis, we have seen that this variable also has the thickest tails in the probability distributions, meaning that 12-month libor returns have the highest power law features within the series. © 2015, CIBER Institute. All rights reserved.