arXiv research

Study finds time-varying volatility and multifractality in Bitcoin, with asymmetry weakening as market efficiency increases.

Bitcoin volatility shows multifractal structure, contradicting rough volatility models.

Bitcoin volatility analysis shows decreasing HE with longer sampling periods.

Quantum circuits predict volatility dynamics preserving asymmetry.

Recent studies have found that the log-volatility of asset returns exhibit roughness. This study investigates roughness or the anti-persistence of Bitcoin volatility. Using the multifractal detrended fluctuation analysis, we obtain the generalized Hurst exponent of the log-volatility increments and find that the genera…

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 effect and the multifractal nature. By investigating the autocorrelation functi…

We introduce tools for inference in the multifractal random walk introduced by Bacry et al. (2001). These tools include formulas for smoothing, filtering and volatility forecasting. In addition, we present methods for computing conditional densities for one- and multi-step returns. The inference techniques presented in…

Many financial variables are found to exhibit multifractal nature, which is usually attributed to the influence of temporal correlations and fat-tailedness in the probability distribution (PDF). Based on the partition function approach of multifractal analysis, we show that there is a marked finite-size effect in the d…

A model explains stock returns and volatility using multifractal and rough components.

A new model captures multifractal volatility in stock returns.

A new model captures multifractal volatility in stock returns.

The inversion formula for conservative multifractal measures was unveiled mathematically a decade ago, which is however not well tested in real complex systems. In this Letter, we propose to verify the inversion formula using high-frequency turbulent financial data. We construct conservative volatility measure based on…

Digital currencies exhibit multifractality due to heavy-tailed returns and temporal correlations.

We study the problem of forecasting volatility for the multifractal random walk model. In order to avoid the ill posed problem of estimating the correlation length T of the model, we introduce a limiting object defined in a quotient space; formally, this object is an infinite range logvolatility. For this object and th…

We have performed detailed multifractal analysis on the minutely volatility of two indexes and 1139 stocks in the Chinese stock markets based on the partition function approach. The partition function $χ_q(s)$ scales as a power law with respect to box size $s$. The scaling exponents $τ(q)$ form a nonlinear function of …

Complex systems are composed of mutually interacting components and the output values of these components are usually long-range cross-correlated. We propose a method to characterize the joint multifractal nature of such long-range cross correlations based on wavelet analysis, termed multifractal cross wavelet analysis…

Model predicts stock price volatility using stochastic differential equations.

Many complex systems generate multifractal time series which are long-range cross-correlated. Numerous methods have been proposed to characterize the multifractal nature of these long-range cross correlations. However, several important issues about these methods are not well understood and most methods consider only o…

By adopting Multifractal detrended fluctuation (MF-DFA) analysis methods, the multifractal nature is revealed in the high-frequency data of two typical indexes, the Shanghai Stock Exchange Composite 180 Index (SH180) and the Shenzhen Stock Exchange Composite Index (SZCI). The characteristics of the corresponding multif…

Introduces log S-fBM model to unify rough and multifractal volatility.

In the canonical framework, we propose an alternative approach for the multifractal analysis based on the detrending moving average method (MF-DMA). We define a canonical measure such that the multifractal mass exponent $τ(q)$ is related to the partition function and the multifractal spectrum $f(α)$ can be directly det…

An empirical algorithm is used here to study the stochastic and multifractal nature of nonlinear time series. A parameter can be defined to quantitatively measure the deviation of the time series from a Wiener process so that the stochasticity of different time series can be compared. The local volatility of the time s…

This is a short review in honor of B. Mandelbrot's 80st birthday, to appear in W ilmott magazine. We discuss how multiplicative cascades and related multifractal ideas might be relevant to model the main statistical features of financial time series, in particular the intermittent, long-memory nature of the volatility.…

In this manuscript we present a comprehensive study on the multifractal properties of high-frequency price fluctuations and instantaneous volatility of the equities that compose Dow Jones Industrial Average. The analysis consists about quantification of dependence and non-Gaussianity on the multifractal character of fi…

Study finds multifractal cross-correlations between agricultural markets and external uncertainties.

In this paper we briefly review the recently inrtroduced Multifractal Random Walk (MRW) that is able to reproduce most of recent empirical findings concerning financial time-series : no correlation between price variations, long-range volatility correlations and multifractal statistics. We then focus on its extension t…

Using 1-min returns of Bitcoin prices, we investigate statistical properties and multifractality of a Bitcoin time series. We find that the 1-min return distribution is fat-tailed, and kurtosis largely deviates from the Gaussian expectation. Although for large sampling periods, kurtosis is anticipated to approach the G…

By applying the multifractal detrended fluctuation analysis to the high-frequency tick-by-tick data from Deutsche Börse both in the price and in the time domains, we investigate multifractal properties of the time series of logarithmic price increments and inter-trade intervals of time. We show that both quantities rev…

Mutually interacting components form complex systems and the outputs of these components are usually long-range cross-correlated. Using wavelet leaders, we propose a method of characterizing the joint multifractal nature of these long-range cross correlations, a method we call joint multifractal analysis based on wavel…

We investigate multifractality in the Korean stock-market index KOSPI. The generalized $q$th order height-height correlation function shows multiscaling properties. There are two scaling regimes with a crossover time around $t_c =40$ min. We consider the original data sets and the modified data sets obtained by removin…

Financial volatility risk and its relation to a business cycle-related intrinsic time is addressed through a multiple round evolutionary quantum game equilibrium leading to turbulence and multifractal signatures in the financial returns and in the risk dynamics. The model is simulated and the results are compared with …

This paper proposes a new framework for financial risk that considers predictability rather than volatility.

We study, both analytically and numerically, an ARCH-like, multiscale model of volatility, which assumes that the volatility is governed by the observed past price changes on different time scales. With a power-law distribution of time horizons, we obtain a model that captures most stylized facts of financial time seri…

This study examines asymmetric cross-correlations in cryptocurrency markets using fractal analysis.

We present an approximated maximum likelihood method for the multifractal random walk processes of [E. Bacry et al., Phys. Rev. E 64, 026103 (2001)]. The likelihood is computed using a Laplace approximation and a truncation in the dependency structure for the latent volatility. The procedure is implemented as a package…

Multifractal processes are a relatively new tool of stock market analysis. Their power lies in the ability to take multiple orders of autocorrelations into account explicitly. In the first part of the paper we discuss the framework of the Lux model and refine the underlying phenomenological picture. We also give a proc…

Study examines how COVID-19 affected stock and crypto market efficiency.

Analyzed Bitcoin market index volatility changes over two distinct periods using anomalous diffusion and multifractal analysis.

Study examines how Trump tariffs and COVID-19 affected financial market efficiency.

In this paper it was developed a modification of the known multiagent model Minority Game, designed to simulate the behavior of traders in financial markets and the resulting price dynamics on the abstract resource. The model was implemented in the form of software. The modified version of Minority Game was investigate…

The study examines cryptocurrency market activity, revealing multifractal inter-transaction times and challenging traditional statistical models.

The statistical properties of the multipliers of the absolute returns are investigated using one-minute high-frequency data of financial time series. The multiplier distribution is found to be independent of the box size $s$ when $s$ is larger than some crossover scale, providing direct evidence of the existence of sca…

Modeling price formation with interacting Hawkes processes leading to stochastic volatility with leverage.

There are a number of situations in which several signals are simultaneously recorded in complex systems, which exhibit long-term power-law cross-correlations. The multifractal detrended cross-correlation analysis (MF-DCCA) approaches can be used to quantify such cross-correlations, such as the MF-DCCA based on detrend…

We extend and test empirically the multifractal model of asset returns based on a multiplicative cascade of volatilities from large to small time scales. The multifractal description of asset fluctuations is generalized into a multivariate framework to account simultaneously for correlations across times scales and bet…

Study cryptocurrency market complexity using multifractal and cross-correlation analyses.

Cryptocurrencies show mature market characteristics but vary by size.

Previous studies indicate that nonlinear properties of Gaussian time series with long-range correlations, $u_i$, can be detected and quantified by studying the correlations in the magnitude series $|u_i|$, i.e., the ``volatility''. However, the origin for this empirical observation still remains unclear, and the exact …