Visual information and expert’s idea in Hurst index estimation of the fractional Brownian motion using a diffusion type approximation

Taheriyoun, Ali Reza; Moghimbeygi, Meisam

doi:10.1038/srep42482

Cited by 5 publications

(4 citation statements)

References 31 publications

(34 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Such a combination, possible also with future works, would yield a systematic model selection among a large set of models for single particle tracking data. We also note that a number of previous works on the aspect of parameter estimation for FBM by Bayesian methods have been published previously, for instance [24][25][26].…”

Section: Introductionmentioning

confidence: 88%

Bayesian model selection with fractional Brownian motion

Krog¹,

Jacobsen²,

Lund³

et al. 2018

J. Stat. Mech.

View full text Add to dashboard Cite

We implement Bayesian model selection and parameter estimation for the case of fractional Brownian motion with measurement noise and a constant drift. The approach is tested on artificial trajectories and shown to make estimates that match well with the underlying true parameters, while for model selection the approach has a preference for simple models when the trajectories are finite. The approach is applied to observed trajectories of vesicles diffusing in Chinese hamster ovary cells.Here it is supplemented with a goodness-of-fit test, which is able to reveal statistical discrepancies between the observed trajectories and model predictions.arXiv:1804.01365v1 [physics.data-an]

show abstract

Section: Introductionmentioning

confidence: 88%

Bayesian model selection with fractional Brownian motion

Krog¹,

Jacobsen²,

Lund³

et al. 2018

J. Stat. Mech.

View full text Add to dashboard Cite

show abstract

“…For a stationary Gaussian random field, Wu & Lim (2016) used the decay rate of the spectral density to estimate the fractal dimension. Wang (1997) proposed a wavelet shrinkage estimator for noisy observations of a stochastic process and the extension to N ‐dimensional random fields was developed by Taheriyoun & Wang (2017). The fractal index has also been estimated as the self‐similarity index in a frequency‐domain using wavelets for time series data by Ramírez‐Cobo et al (2011).…”

Section: Introductionmentioning

confidence: 99%

“…For a specific case of semistationary Brownian motions, Bennedsen et al (2019) proposed a test for the roughness of the time series using the value of the fractal index. The Bayesian approach in estimation of the fractal index has only been studied for fractional Brownian motion (Carlin & Dempster, 1989; Taheriyoun & Moghimbeygi, 2017; Chen, Shafie & Lin, 2017) particularly in physics (Krog et al, 2018). We refer to Gneiting, Ševčíková & Percival (2012) and the references therein for a comprehensive review on various estimators of fractal dimension.…”

Section: Introductionmentioning

confidence: 99%

The estimation of the fractal dimension of a Gaussian field via Euler characteristic

Taheriyoun

Shafie

2021

Can J Statistics

View full text Add to dashboard Cite

Fractal dimension is a useful characteristic for measuring the irregularity of random fields. In this work, we employ the Euler characteristic (EC) of the excursion sets of a field to estimate the fractal dimension of the random field using the roughness of the underlying realization. The EC of a non‐differentiable Gaussian field is either zero or infinity with probability one and hence we employ a weighted smooth version of the field. Under some weak assumptions, the estimator is consistent when the weight function is constant. The results are examined through a simulation study and applied on real data.

show abstract

“…Fractal has achieved great success in the fields of modeling complex natural scenes, texture analysis, and measuring the length of complex curves. 7 Fractal objects have their own dimensions, called fractal dimensions, which are the most basic quantities to quantitatively represent self-similar random fractal states, usually non-integer dimensions, which are smaller than the number of dimensions and is greater than topological dimension. In Euclidean space, the dimension of a geometric figure is an integer value, while the dimension in fractal theory can be a fractional value.…”

Section: Introductionmentioning

confidence: 99%

Application of Fractal Dimension of Fractional Brownian Motion to Supply Chain Financing and Operational Comprehensive Decision-Making

2020

View full text Add to dashboard Cite

For a long time, the mismatch between material flow and capital flow in the supply chain operation management practice is very prominent, which has led to the inefficiency of supply chain operation and hindered the exertion of supply chain’s advantages. In the field of supply chain management theory research, the information completeness in capital market has long been a hypothetical premise, which has led to the separation of corporate financing and operational decision-making research. In addition to production, inventory, procurement, pricing and other strategies in supply chain operations, payment options and credit incentives are also important decisions for both parties, especially for products with long production and sales cycles; different payment methods directly affect corporate capital flows and the enterprise’s long-term development. On the basis of summarizing and analyzing previous works, this paper analyzed the research status and significance of supply chain financing and operational comprehensive decision-making, expounded the development background, current situation, and future challenges of the fractal dimension of fractional Brownian motion; elaborated the principles and methods of the scaling properties of fractional Brownian motion and the phase space reconstruction of time series, established a financial management analysis model based on the fractal dimension of fractional Brownian motion, performed the analysis of the agglomeration degree, time series and multi-fractal characteristics of supply chain financing, explored the coupling relationship between the comprehensive operational decision-making and Brownian motion’s scaling properties. The final empirical analysis showed that when own funds are sufficient, the production should be carried out with the goal of maximizing profits, and full consideration should be given customer channel stickiness, relative costs of offline and online channel products, and product profitability; the proposed analysis model can achieve the optimal order quantity in supply chain, and reach risk and benefit sharing among financial institutions, retailers, and suppliers by setting the financing interest rate, wholesale price, repurchase price and other parameters, thereby improving supply chain performance. This study results of this paper provided a reference for further researches on the application of fractal dimension of the fractional Brownian motion to the supply chain financing and operational comprehensive decision-making.

show abstract

Visual information and expert’s idea in Hurst index estimation of the fractional Brownian motion using a diffusion type approximation

Cited by 5 publications

References 31 publications

Bayesian model selection with fractional Brownian motion

Bayesian model selection with fractional Brownian motion

The estimation of the fractal dimension of a Gaussian field via Euler characteristic

Application of Fractal Dimension of Fractional Brownian Motion to Supply Chain Financing and Operational Comprehensive Decision-Making

Contact Info

Product

Resources

About