A comparison of maximum likelihood and absolute moments for the estimation of Hurst exponents in a stationary framework

Garcin, Matthieu

doi:10.1016/j.cnsns.2022.106610

Cited by 6 publications

(4 citation statements)

References 30 publications

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“…On the other hand, when θ > 1, the minimum information is reached for H → 1 and, as soon as θ is large enough, the maximum information corresponds both to H → 0 and H = 1/2. This apparent contradiction with the traditional interpretation of the Hurst exponent is in fact clearly established in the literature devoted to this model [29,31]. The parameter H is related to the fractal properties of the process B H t , not to the fractal properties of X H,θ t .…”

Section: Log-prices Following a Stationary Delampertized Fbmcontrasting

confidence: 67%

“…Some extensions and transformations of the fBm make it possible to consider more general dynamics with some fractal features or even with more complex multifractal properties [59,41,22,37]. One can cite for instance stationary transformations [16,40,29,31], non-Gaussian extensions [61,64,3], Hurst exponents varying through time in a deterministic [18,11,28] or stochastic fashion [12,13,30], and the multifractal random walk [6,5,53].…”

Section: Market Information Of Fractal Dynamicsmentioning

confidence: 99%

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Maxwell’s Demon and Information Theory in Market Efficiency: A Brillouin’s Perspective

Brouty

Garcin

2022

The 41st International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering

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Section: Log-prices Following a Stationary Delampertized Fbmcontrasting

confidence: 67%

Section: Market Information Of Fractal Dynamicsmentioning

confidence: 99%

Maxwell’s Demon and Information Theory in Market Efficiency: A Brillouin’s Perspective

Brouty

Garcin

2022

The 41st International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering

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“…But this practical limitation does not come from a particular property of the fBm itself. It comes instead from the fact that the model is not well specified or from the related difficulties to estimate the parameters properly, in a nutshell from model risk [23,24]. Besides the identification of market efficiency to long-range dependence, another branch of the econophysics literature considers that the market is efficient for H = 1/2 and that its inefficiency gradually increases as H gets away from 1/2 [33,34,32,10,5].…”

Section: Introductionmentioning

confidence: 99%

Forecasting with fractional Brownian motion: a financial perspective

Garcin

2022

Quantitative Finance

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The fractional Brownian motion (fBm) extends the standard Brownian motion by introducing some dependence between non-overlapping increments. Consequently, if one considers for example that log-prices follow an fBm, one can exploit the non-Markovian nature of the fBm to forecast future states of the process and make statistical arbitrages. We provide new insights into forecasting an fBm, by proposing theoretical formulas for accuracy metrics relevant to a systematic trader, from the hit ratio to the expected gain and risk of a simple strategy. In addition, we answer some key questions about optimizing trading strategies in the fBm framework: Which lagged increments of the fBm, observed in discrete time, are to be considered? If the predicted increment is close to zero, up to which threshold is it more profitable not to invest? We also propose empirical applications on high-frequency FX rates, as well as on realized volatility series, exploring the rough volatility concept in a forecasting perspective.

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“…From the perspective of Garcin (2022), this method allows the researcher to make a good assessment of the model specification, and is a generalization of the aggregate variance method as it uses the same principle as 𝑋 𝑚 (Aldea and Tarniceriu 2013).…”

Section: Absolute Moments Methodsmentioning

confidence: 99%

Analysis of similarities in respiratory tract genomes: an approach using the Hurst exponent and the non-decimated discrete wavelet transform

Ernesto,

Ferreira,

Sáfadi

2023

Cad. Pedagógico

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The implementation of statistical methods that can make the similarity study process more efficient has been very common in current research, because some methods such as wavelets make the processing of data manipulation faster and with the ability to process thousands of nucleotides in a genomic sequencing, and consequently better estimates are obtained. Thus, this work aimed to analyze some genomes of the Coronaviridae family and the Paramyxoviridae family, looking for similarities through signal decomposition considering the non-decimated discrete wavelet transform techniques. The entire genome sequences of the families were initially extracted from the NCBI website and then pattern analysis was performed using a signal processing method, based on the GC content. For each GC sequence, decomposition was performed using the six-level discrete non-decimated Daubechies wavelet transform. Then, the Hurst exponent was calculated for each level of decomposition and the sequences were verified with similar patterns. After the cluster analysis, it was possible to obtain that the pair Bet1 and MERS proved to be similar in almost all methods, the other pair of sequences that proved to be similar by the absolute moments methods and by the aggregated variance method was the pair Gamma1 and Del, the group composed of Influ1, Influ4, Influ3 and Hendra was similar by the absolute moments methods, aggregated variance, and in the R/S analysis method, there was a substitution of Influ4 by Influ5. At the end of the study, it was possible to conclude that the non-decimated discrete wavelet transform allowed us to decompose each one of the sequences and, consequently, a more detailed study of similarity can be carried out, and it was possible to obtain, by some methods, strains of Coronaviridae that do not resemble the strains of Paramyxoviridae.

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A comparison of maximum likelihood and absolute moments for the estimation of Hurst exponents in a stationary framework

Cited by 6 publications

References 30 publications

Maxwell’s Demon and Information Theory in Market Efficiency: A Brillouin’s Perspective

Maxwell’s Demon and Information Theory in Market Efficiency: A Brillouin’s Perspective

Forecasting with fractional Brownian motion: a financial perspective

Analysis of similarities in respiratory tract genomes: an approach using the Hurst exponent and the non-decimated discrete wavelet transform

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