In this paper, we show how the sampling properties of the Hurst exponent methods of estimation change with the presence of heavy tails. We run extensive Monte Carlo simulations to find out how rescaled range analysis (R/S), multifractal detrended fluctuation analysis (MF-DFA), detrending moving average (DMA) and genera…
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48 results for “Hurst exponent”
Hurst exponent and prediction based on weak-form efficient market hypothesis of stock marketsq-fin.ST
We empirically investigated the relationships between the degree of efficiency and the predictability in financial time-series data. The Hurst exponent was used as the measurement of the degree of efficiency, and the hit rate calculated from the nearest-neighbor prediction method was used for the prediction of the dire…
Optimizing Returns Using the Hurst Exponent and Q Learning on Momentum and Mean Reversion Strategiesq-fin.ST
Optimizes trading returns using Hurst exponent and Q-learning.
problem Maximizing returns from momentum and mean reversion strategies.
method Classifies assets using Hurst exponent and uses Q-learning to improve trading algorithms.
result Trading with Hurst exponent can achieve higher returns but at higher risk.
mfBm models and forecasts volatility with different Hurst exponents and correlations.
problem Modeling and forecasting volatility with varying Hurst exponents and correlations.
method Multivariate fractional Brownian motion (mfBm) with component-wise Hurst exponents, novel estimation method, time-reversibility test.
result mfBm reduces forecasting errors compared to a one-dimensional model and outperforms HAR model.
Python package for estimating Hurst exponent in fBm.
problem Estimating Hurst exponent in fractional Brownian motion.
method Whittle's likelihood method applied to fractional Gaussian noise.
result Implementation achieves state-of-the-art accuracy and speed.
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 series is anti-persistent. After 2013, as liquidity increased, the Hurst exponent ro…
We apply the Hurst exponent idea for investigation of DJIA index time-series data. The behavior of the local Hurst exponent prior to drastic changes in financial series signal is analyzed. The optimal length of the time-window over which this exponent can be calculated in order to make some meaningful predictions is di…
The common assumption of universal behavior in stock market data can sometimes lead to false conclusions. In statistical physics, the Hurst exponents characterizing long-range correlations are often closely related to universal exponents. We show, that in the case of time series of the traded value, these Hurst exponen…
We investigate the use of the Hurst exponent, dynamically computed over a moving time-window, to evaluate the level of stability/instability of financial firms. Financial firms bailed-out as a consequence of the 2007-2010 credit crisis show a neat increase with time of the generalized Hurst exponent in the period prece…
Noise-resilient method improves Hurst exponent estimation accuracy in noisy data.
problem Noise degrades accuracy of Hurst exponent estimation methods.
method Noise-Controlled ALPHEE (NC-ALPHEE) using wavelet multi-scale analysis and neural network combination.
result NC-ALPHEE consistently outperforms existing techniques in noisy conditions.
This paper investigates the relationship between price multiscaling and volatility roughness in financial markets.
problem The inability of traditional models to capture financial stylized facts like volatility roughness and multiscaling.
method Simulation experiments and real data analysis using a rough volatility model.
result The rough volatility model fails to reproduce the multiscaling features of real data, indicating a negative interplay between multiscaling and volatility roughness.
Rough volatility of Bitcoinq-fin.ST
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…
Multifractal Features in the Foreign Exchange and Stock Marketscond-mat.stat-mech
The multifractal behavior for tick data of prices is investigated in Korean financial market. Using the rescaled range analysis(R/S analysis), we show the multifractal nature of returns for the won-dollar exchange rate and the KOSPI. We also estimate the Hurst exponent and the generalized th-order Hurst exponent in …
We empirically analyze the most volatile component of the electricity price time series from two North-American wholesale electricity markets. We show that these time series exhibit fluctuations which are not described by a Brownian Motion, as they show multi-scaling, high Hurst exponents and sharp price movements. We …
Study examines how COVID-19 affected stock and crypto market efficiency.
problem Impact of COVID-19 on market efficiency of different asset classes.
method Analysis of price returns, absolute returns, and volatility increments in stock and cryptocurrency markets.
result Market efficiency varied by asset class and market, with some time series showing gradual decline over time.
An exclusion particle model is considered as a highly simplified model of a limit order market. Its price behavior reproduces the well known crossover from over-diffusion (Hurst exponent H>1/2) to diffusion (H=1/2) when the time horizon is increased, provided that orders are allowed to be canceled. For early times a ma…
A new model captures multifractal volatility in stock returns.
problem Capturing multifractal volatility in stock returns.
method Introduced mLog S-fBM model, defined mS-fBM, and developed calibration procedure.
result Model captures multifractal behavior in stock returns, validating on real data.
A new option pricing model uses a time-varying Hurst exponent for more accurate financial predictions.
problem Inaccurate modeling of financial time series due to constant memory parameter limitations.
method Modeling price fluctuations with multifractional Brownian motion and deriving option pricing formula.
result Empirical performance shows the multifractional model fits market quotes better than standard models.
In recent years a new type of tradable assets appeared, generically known as cryptocurrencies. Among them, the most widespread is Bitcoin. Given its novelty, this paper investigates some statistical properties of the Bitcoin market. This study compares Bitcoin and standard currencies dynamics and focuses on the analysi…
A new model captures multifractal volatility in stock returns.
problem Capturing multifractal volatility in stock returns.
method Introduced mLog S-fBM model, defined mS-fBM, and developed calibration procedure.
result Validated model on synthetic and real data, showing multifractal behavior.
A model explains stock returns and volatility using multifractal and rough components.
problem Reconciling multifractal stock returns and rough index volatilities.
method Nested factor model with multifractal and rough volatility components.
result The model explains stock index Hurst exponents larger than individual stock exponents.
We give a stochastic microscopic modelling of stock markets driven by continuous double auction. If we take into account the mimetic behavior of traders, when they place limit order, our virtual markets shows the power-law tail of the distribution of returns with the exponent outside the Levy stable region, the short m…
The local Hurst exponent, a measure employed to detect the presence of dependence in a time series, may also be used to investigate the source of intraday variation observed in the returns in foreign exchange markets. Given that changes in the local Hurst exponent may be due to either a time-varying range, or standard …
Study finds roughness in volatility despite diffusive instantaneous volatility.
problem Determining the roughness of volatility in financial assets.
method Non-parametric method based on normalized -th variation for estimating roughness of sample paths.
result Realized volatility exhibits rough behavior with a significantly smaller Hurst exponent than instantaneous volatility.
We report an empirical study of the Ibovespa index of the Sao Paulo Stock Exchange in which we detect the existence of long-range correlations. To analyze our data we introduce a rescaled variant of the usual Detrended Fluctuation Analysis that allows us to obtain the Hurst exponent through a one-parameter fitting. We …
Relative cluster entropy for power-law correlated sequencescond-mat.stat-mech
A measure called relative cluster entropy distinguishes between correlated and uncorrelated sequences.
problem Distinguishing between sequences with different correlation degrees.
method Minimum relative entropy principle applied to cluster partitions of power-law correlated sequences.
result Optimal Hurst exponents are selected for market price series, indicating non-markovianity.
Adaptive estimation of alpha-Stable distribution and Hurst exponent for nonstationary time series.
problem Nonstationary time series require adaptive models to avoid bias.
method Moving estimator with exponentially weakening weights of old values, optimized using EMA of absolute central moments.
result Continuous adaptive estimation of alpha-Stable distribution and Hurst exponent for market stability evaluation.
A new method uses burst and inter-burst duration to test long-range memory in financial markets.
problem Varying results from long-range memory estimators in financial markets.
method Burst and inter-burst duration statistical analysis of limit order book data.
result The new method provides a more reliable evaluation of the Hurst exponent.
This study investigates empirically whether the degree of stock market efficiency is related to the prediction power of future price change using the indices of twenty seven stock markets. Efficiency refers to weak-form efficient market hypothesis (EMH) in terms of the information of past price changes. The prediction …
Study examines cryptocurrency behavior during and after the pandemic.
problem Impact of the pandemic on cryptocurrency long-term memory and volatility.
method Used wavelet-based Hurst exponent analysis on eleven important coins.
result Long-term memory of returns mildly affected during pandemic, but volatility suffered temporary impact.
Integrating the implied regularity into implied volatility models: A study on free arbitrage modelq-fin.CP
Study integrates implied Hurst exponent into IV models for better market efficiency.
problem Capturing market efficiency in IV models based on moneyness.
method Developed an IV model integrating implied Hurst exponent H, optimizing across multiple indexes.
result Model outperforms SABR and fSABR in accuracy, capturing IV-H dynamics.
Estimates Hurst exponent of log-volatility using KS statistic, addressing serial correlation in financial data.
problem Estimating Hurst exponent of log-volatility in financial time series with serial correlation.
method Proposes a random permutation procedure to remove serial correlation, using the Kolmogorov-Smirnov statistic for distribution-based estimation.
result Establishes the asymptotic variance of the estimator and reveals statistically significant hierarchy of roughness in volatility measures.
Study the link between entropy and market efficiency using fractal properties.
problem Determining market efficiency using entropy-based measures and fractal properties.
method Theoretical expression for market information using fractional Brownian motion and Lamperti transform. Multiscale method to interpret entropy and market information.
result A Hurst exponent close to 1/2 can lead to high informativeness of time series due to stationarity.
The Chirikov standard map and the 2D Froeschlé map are investigated. A few thousand values of the Hurst exponent (HE) and the maximal Lyapunov exponent (mLE) are plotted in a mixed space of the nonlinear parameter versus the initial condition. Both characteristic exponents reveal remarkably similar structures in this s…
On the interplay between short and long term memory in the power-law cross-correlations settingstat.ME
We focus on emergence of the power-law cross-correlations from processes with both short and long term memory properties. In the case of correlated error-terms, the power-law decay of the cross-correlation function comes automatically with the characteristics of separate processes. Bivariate Hurst exponent is then equa…
Algorithm identifies fractal system's scaling exponents in high dimensions.
problem Statistical identification of Hurst distribution in high-dimensional fractal systems.
method Wavelet random matrices, modified spectral clustering, model selection.
result Algorithm consistently estimates Hurst distribution in moderately high dimensions.
The market efficiency hypothesis has been proposed to explain the behavior of time series of stock markets. The Black-Scholes model (B-S) for example, is based on the assumption that markets are efficient. As a consequence, it is impossible, at least in principle, to "predict" how a market behaves, whatever the circums…
Multifractal Measures for the Yen-Dollar Exchange Ratecond-mat.stat-mech
We study the tick dynamical behavior of the yen-dollar exchange rate using the rescaled range analysis in financial market. It is found that the multifractal Hurst exponents with the short and long-run memory effects can be obtained from the yen-dollar exchange rate. This exists one crossover for the Hurst exponents at…
The speculation game is an agent-based toy model to investigate the dynamics of the financial market. Our model has achieved the reproduction of 10 of the well-known stylized facts for financial time series. However, there is also a divergence from the behavior of real market. The market price of the model tends to be …
We introduce two new estimators of the bivariate Hurst exponent in the power-law cross-correlations setting -- the cross-periodogram and local -Whittle estimators -- as generalizations of their univariate counterparts. As the spectrum-based estimators are dependent on a part of the spectrum taken into consideration …
Multiscale Markowitzq-fin.PM
This paper improves traditional Markowitz optimization by considering variance at multiple time scales.
problem Traditional Markowitz optimization limits to a single time scale, ignoring variance across different frequencies.
method Introduces multifrequency optimization allowing specification of target Hurst exponents across multiple time scales.
result Effective risk management strategy that aligns with investor preferences at various time scales.
A comparison among some Hurst exponent approaches to predict nascent bubbles in company stocksq-fin.ST
In this paper, three approaches to calculate the self-similarity exponent of a time series are compared in order to determine which one performs best to identify the transition from random efficient market behavior (EM) to herding behavior (HB) and hence, to find out the beginning of a market bubble. In particular, cla…
The conventional formal tool to detect effects of the financial persistence is in terms of the Hurst exponent. A typical corresponding result is that its value comes out close to 0.5, as characteristic for geometric Brownian motion, with at most small departures from this value in either direction depending on the mark…
Strategy for investments from Zipf law(s)cond-mat.stat-mech
We have applied the Zipf method to extract the exponent for seven financial indices (DAX, FTSE; DJIA, NASDAQ, S&P500; Hang-Seng and Nikkei 225), after having translated the signals into a text based on two letters. We follow considerations based on the signal Hurst exponent and the notion of a time dependent Zipf …
We reanalyze high resolution data from the New York Stock Exchange and find a monotonic (but not power law) variation of the mean value per trade, the mean number of trades per minute and the mean trading activity with company capitalization. We show that the second moment of the traded value distribution is finite. Co…
Bitcoin volatility analysis shows decreasing HE with longer sampling periods.
problem Understanding volatility patterns in Bitcoin using different sample sizes.
method Examined Bitcoin data to analyze Hurst exponent (HE) and multifractality.
result HE decreases as sampling period increases, indicating rough volatility.
This paper investigates the presence of long memory in corporate bond and stock indices of six European Union countries from July 1998 to February 2015. We compute the Hurst exponent by means of the DFA method and using a sliding window in order to measure long range dependence. We detect that Hurst exponents behave di…
The state of a stochastic process evolving over a time is typically assumed to lie on a normal distribution whose width scales like . However, processes where the probability distribution is not normal and the scaling exponent differs from are known. The search for possible origins of such "a…