Estimating the Parameters of a Fractional Brownian Motion by Discrete Variations of its Sample Paths

By Jean‐François Coeurjolly. 2001

220 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d7caf8c4203ea8e3059bfdeef369bda62d7307a3

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Citations in the corpus

Volatility is rough (2014, unknown): “In a pioneering paper, Comte and Renault (1998) proposed to model log-volatility using fractional Brownian motion (fBm for short), ensuring long memory by choosing the Hurst parameter H > 1/2.”
Variations and estimators for selfsimilarity parameters via Malliavin calculus (2009, background): “A detailed study can be found in [8] and [11] or, more recently, in [4].”
Pathwise Identification Of The Memory Function Of Multifractional Brownian Motion With Application To Finance (2005, background): “This problem has been solved by Coeurjolly [11] in a more general estimation context at the cost of reducing the rate of convergence of the estimator.”
Statistical inference for Vasicek-type model driven by Hermite processes (2017, background): “Our paper is relevant to the literature on parameter estimation for processes with Gaussian and non-Gaussian long-memory processes, including [1, 5, 6, 7, 8, 9, 12, 13, 14, 16, 27].”
Estimators of Fractal Dimension: Assessing the Roughness of Time Series and Spatial Data (2011, background): “The general case, p > 0, has been studied by Coeurjolly (2001, 2008).”
Variations and Hurst index estimation for a Rosenblatt process using longer filters (2009, background): “(4) There exists a direct connection between the behavior of the variations and the convergence of an estimator for the selfsimilarity order based on these variations (see [7, 28]): if the renormalized variation satisfies a central limit theorem then so does the estimator, a desirable fact for stati”
A least square-type procedure for parameter estimation in stochastic differential equations with additive fractional noise (2011, background): “Date: November 8, 2011.”
Self-similarity parameter estimation and reproduction property for non-Gaussian Hermite processes (2008, methodology): “2, page 492 in [6] and it can be used exactly as in the proof of Proposition 1 in [4].”