Simulation and identification of the fractional Brownian motion: a bibliographical and comparative study

Citations

Cited by:

1. Neuenkirch, Andreas, 2008. "Optimal pointwise approximation of stochastic differential equations driven by fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2294-2333, December.
2. Marina Resta & Davide Sciutti, 2003. "Spot price dynamics in deregulated power markets," Econometrics 0312002, University Library of Munich, Germany.
3. Jean-Christophe Breton & Jean-François Coeurjolly, 2012. "Confidence intervals for the Hurst parameter of a fractional Brownian motion based on finite sample size," Statistical Inference for Stochastic Processes, Springer, vol. 15(1), pages 1-26, April.
4. Skorniakov, V., 2019. "On a covariance structure of some subset of self-similar Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 129(6), pages 1903-1920.
5. Bianchi, Sergio, 2004. "A new distribution-based test of self-similarity," MPRA Paper 16640, University Library of Munich, Germany.
6. Zunino, Luciano & Tabak, Benjamin M. & Serinaldi, Francesco & Zanin, Massimiliano & Pérez, Darío G. & Rosso, Osvaldo A., 2011. "Commodity predictability analysis with a permutation information theory approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(5), pages 876-890.
7. Bondarenko, Valeria & Bondarenko, Victor & Truskovskyi, Kyryl, 2017. "Forecasting of time data with using fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 97(C), pages 44-50.
8. Ahmadian, D. & Ballestra, L.V. & Shokrollahi, F., 2022. "A Monte-Carlo approach for pricing arithmetic Asian rainbow options under the mixed fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
9. Xu, Weijun & Sun, Qi & Xiao, Weilin, 2012. "A new energy model to capture the behavior of energy price processes," Economic Modelling, Elsevier, vol. 29(5), pages 1585-1591.
10. Wang, Xiaohu & Xiao, Weilin & Yu, Jun, 2023. "Modeling and forecasting realized volatility with the fractional Ornstein–Uhlenbeck process," Journal of Econometrics, Elsevier, vol. 232(2), pages 389-415.
11. Peter Kloeden & Andreas Neuenkirch & Raffaella Pavani, 2011. "Multilevel Monte Carlo for stochastic differential equations with additive fractional noise," Annals of Operations Research, Springer, vol. 189(1), pages 255-276, September.
12. Kubilius, K. & Mishura, Y., 2012. "The rate of convergence of Hurst index estimate for the stochastic differential equation," Stochastic Processes and their Applications, Elsevier, vol. 122(11), pages 3718-3739.
13. repec:jss:jstsof:23:i01 is not listed on IDEAS
14. Jean-François Coeurjolly, 2001. "Estimating the Parameters of a Fractional Brownian Motion by Discrete Variations of its Sample Paths," Statistical Inference for Stochastic Processes, Springer, vol. 4(2), pages 199-227, May.
15. Sebastian Michalski, 2006. "Blocks adjustment – reduction of bias and variance of detrended fluctuation analysis using Monte Carlo simulation," Working Papers 15, Department of Applied Econometrics, Warsaw School of Economics.
16. Marina Resta & Davide Sciutti, "undated". "A characterization of self-affine processes in finance through the scaling function," Modeling, Computing, and Mastering Complexity 2003 13, Society for Computational Economics.
17. Ahmadian, D. & Ballestra, L.V., 2020. "Pricing geometric Asian rainbow options under the mixed fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
18. Andreas Neuenkirch & Ivan Nourdin, 2007. "Exact Rate of Convergence of Some Approximation Schemes Associated to SDEs Driven by a Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 20(4), pages 871-899, December.
19. Michalski, Sebastian, 2008. "Blocks adjustment—reduction of bias and variance of detrended fluctuation analysis using Monte Carlo simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 217-242.
20. Sinn, Mathieu & Keller, Karsten, 2011. "Estimation of ordinal pattern probabilities in Gaussian processes with stationary increments," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1781-1790, April.
21. A. Philippe & E. Thilly, 2002. "Identification of a Locally Self-similar Gaussian Process by Using Convex Rearrangements," Methodology and Computing in Applied Probability, Springer, vol. 4(2), pages 195-209, June.
22. Bibinger, Markus, 2020. "Cusum tests for changes in the Hurst exponent and volatility of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 161(C).
23. Matthieu Garcin & Martino Grasselli, 2020. "Long vs Short Time Scales: the Rough Dilemma and Beyond," Papers 2008.07822, arXiv.org, revised Nov 2021.
24. John-Fritz Thony & Jean Vaillant, 2022. "Parameter Estimation for a Fractional Black–Scholes Model with Jumps from Discrete Time Observations," Mathematics, MDPI, vol. 10(22), pages 1-17, November.
25. Sikora, Grzegorz, 2018. "Statistical test for fractional Brownian motion based on detrending moving average algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 54-62.
26. Marco Dozzi & Yuliya Mishura & Georgiy Shevchenko, 2015. "Asymptotic behavior of mixed power variations and statistical estimation in mixed models," Statistical Inference for Stochastic Processes, Springer, vol. 18(2), pages 151-175, July.
27. Kozachenko Yuriy & Pashko Anatolii & Vasylyk Olga, 2018. "Simulation of generalized fractional Brownian motion in C([0,T])," Monte Carlo Methods and Applications, De Gruyter, vol. 24(3), pages 179-192, September.
28. repec:jss:jstsof:14:i18 is not listed on IDEAS
29. Sun, Qi & Xu, Weijun & Xiao, Weilin, 2013. "An empirical estimation for mean-reverting coal prices with long memory," Economic Modelling, Elsevier, vol. 33(C), pages 174-181.