Complexity of Financial Time Series: Multifractal and Multiscale Entropy Analyses

TL;DR

This paper compares the complexity of financial time series like Bitcoin, gold, and currency exchange rates using multifractal and multiscale entropy methods, revealing Bitcoin's higher complexity and nonlinear correlations.

Contribution

It applies MF-DFA and RCMSE methods to analyze and compare the complexity of different financial markets, highlighting Bitcoin's unique nonlinear features.

Findings

Bitcoin exhibits higher complexity than other assets.

RCMSE and MF-DFA effectively quantify market complexity.

Higher nonlinear correlations are present in Bitcoin's log-returns.

Abstract

We employed Multifractal Detrended Fluctuation Analysis (MF-DFA) and Refined Composite Multiscale Sample Entropy (RCMSE) to investigate the complexity of Bitcoin, GBP/USD, gold, and natural gas price log-return time series. This study provides a comparative analysis of these markets and offers insights into their predictability and associated risks. Each tool presents a unique method to quantify time series complexity. The RCMSE and MF-DFA methods demonstrate a higher complexity for the Bitcoin time series than others. It is discussed that the increased complexity of Bitcoin may be attributable to the presence of higher nonlinear correlations within its log-return time series.