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Various methods have been developed independently to study the multifractality of measures in many different contexts. Although they all convey the same intuitive idea of giving a "dimension" to sets where a quantity scales similarly within…

Data Analysis, Statistics and Probability · Physics 2017-03-08 Hadrien Salat , Roberto Murcio , Elsa Arcaute

Multifractal Detrended Fluctuation Analysis (MFDFA) is a powerful and widely used technique for characterizing the scaling properties and long-range correlations of complex time series. However, its application often involves significant…

Bid-ask spread is taken as an important measure of the financial market liquidity. In this article, we study the dynamics of the spread return and the spread volatility of four liquid stocks in the Chinese stock market, including the memory…

Statistical Finance · Quantitative Finance 2015-05-30 Tian Qiu , Guang Chen , Li-Xin Zhong , Xiao-Run Wu

Cryptocurrencies gain trust in users by publicly disclosing the full creation and transaction history. In return, the transaction history faithfully records the whole spectrum of cryptocurrency user behaviors. This article analyzes and…

Cryptography and Security · Computer Science 2020-10-05 Xiao Fan Liu , Xin-Jian Jiang , Si-Hao Liu , Chi Kong Tse

Time series of price returns for 80 of the most liquid cryptocurrencies listed on Binance are investigated for the presence of detrended cross-correlations. A spectral analysis of the detrended correlation matrix and a topological analysis…

Statistical Finance · Quantitative Finance 2021-12-14 Jarosław Kwapień , Marcin Wątorek , Stanisław Drożdż

We study quantitatively the level of false multifractal signal one may encounter while analyzing multifractal phenomena in time series within multifractal detrended fluctuation analysis (MF-DFA). The investigated effect appears as a result…

Data Analysis, Statistics and Probability · Physics 2015-06-16 Dariusz Grech , Grzegorz Pamuła

Multifractal Detrended Fluctuation Analysis stands out as one of the most reliable methods for unveiling multifractal properties, specially when real-world time series are under analysis. However, little is known about how several aspects,…

Data Analysis, Statistics and Probability · Physics 2022-07-20 Felipe Olivares , Massimiliano Zanin

We propose a fully multivariate generalization of multifractal detrended fluctuation analysis (MFDFA) and leverage it to develop a fault diagnosis framework for multichannel machine vibration data. We introduce a novel covariance-weighted…

Signal Processing · Electrical Eng. & Systems 2025-11-27 Khuram Naveed , Naveed ur Rehman

Decentralized Finance (DeFi) applications introduce novel financial instruments replicating and extending traditional ones through blockchain-based smart contracts. Among these applications, DeFi derivatives protocols enable the creation…

Computer Science and Game Theory · Computer Science 2026-05-05 Luca Pennella , Pietro Saggese , Fabio Pinelli , Letterio Galletta

In relation to the traditional financial markets, the cryptocurrency market is a recent invention and the trading dynamics of all its components are readily recorded and stored. This fact opens up a unique opportunity to follow the…

Statistical Finance · Quantitative Finance 2023-05-11 Stanisław Drożdż , Jarosław Kwapień , Marcin Wątorek

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…

Statistical Finance · Quantitative Finance 2023-06-29 R. P. Datta

The trustless nature of permissionless blockchains renders overcollateralization a key safety component relied upon by decentralized finance (DeFi) protocols. Nonetheless, factors such as price volatility may undermine this mechanism. In…

General Finance · Quantitative Finance 2021-12-14 Daniel Perez , Sam M. Werner , Jiahua Xu , Benjamin Livshits

The decentralized finance (DeFi) community has grown rapidly in recent years, pushed forward by cryptocurrency enthusiasts interested in the vast untapped potential of new markets. The surge in popularity of cryptocurrency has ushered in a…

Computational Engineering, Finance, and Science · Computer Science 2025-12-12 Adriana Watson , Grant Richards , Daniel Schiff

The prosperity of the cryptocurrency ecosystem drives the need for digital asset trading platforms. Beyond centralized exchanges (CEXs), decentralized exchanges (DEXs) are introduced to allow users to trade cryptocurrency without…

Cryptography and Security · Computer Science 2021-11-12 Pengcheng Xia , Haoyu wang , Bingyu Gao , Weihang Su , Zhou Yu , Xiapu Luo , Chao Zhang , Xusheng Xiao , Guoai Xu

Multifractal analysis is one of the important approaches that enables us to measure the complexity of various data via the scaling properties. We compare the most common techniques used for multifractal exponents estimation from both…

Statistical Finance · Quantitative Finance 2016-10-25 Petr Jizba , Jan Korbel

The miltifractal properties and scaling behaviour of the exchange rate variations of the Iranian rial against the US dollar from a daily perspective is numerically investigated. For this purpose the multifractal detrended fluctuation…

Data Analysis, Statistics and Probability · Physics 2009-11-11 P. Norouzzadeh

The crucial aspect of this demonstration is the discovery of renewal events, hidden in the computed dynamics of a multifractal metronome, which enables the replacement of the phenomenon of strong anticipation with a time delayed…

Adaptation and Self-Organizing Systems · Physics 2017-07-20 Korosh Mahmoodi , Bruce J. West , Paolo Grigolini

This letter investigates the dynamic relationship between market efficiency, liquidity, and multifractality of Bitcoin. We find that before 2013 liquidity is low and the Hurst exponent is less than 0.5, indicating that the Bitcoin time…

Statistical Finance · Quantitative Finance 2020-09-16 Tetsuya Takaishi , Takanori Adachi

In this paper we will try to assess the multifractality displayed by the high-frequency returns of Madrid's Stock Exchange IBEX35 index. A Multifractal Detrended Fluctuation Analysis shows that this index has a wide singularity spectrum…

Statistical Finance · Quantitative Finance 2015-06-16 Pablo Suárez-García , David Gómez-Ullate

The non-fungible token (NFT) market emerges as a recent trading innovation leveraging blockchain technology, mirroring the dynamics of the cryptocurrency market. The current study is based on the capitalization changes and transaction…

Statistical Finance · Quantitative Finance 2024-07-09 Marcin Wątorek , Paweł Szydło , Jarosław Kwapień , Stanisław Drożdż