HURST EXPONENT ESTIMATION OF LOCALLY SELF-SIMILAR GAUSSIAN PROCESSES USING SAMPLE QUANTILES

By Jean‐François Coeurjolly. 2005

55 citations recorded by the source corpus.

This paper is devoted to the introduction of a new class of consistent estimators of the fractal dimension of locally self-similar Gaussian processes. These estimators are based on convex combinations of sample quantiles of discrete variations of a sample path over a discrete grid of the interval $[0,1]$. We derive the almost sure convergence and the asymptotic normality for these estimators. The key-ingredient is a Bahadur representation for sample quantiles of non-linear functions of Gaussians sequences with correlation function decreasing as $k^{-\alpha}L(k)$ for some $\alpha>0$ and some slowly varying function $L(\cdot)$.

Subfields: Economics and Econometrics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7adcac7bded116b6c2ec0a1307e3b51f6c2437fa

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Citations in the corpus

Estimators of Fractal Dimension: Assessing the Roughness of Time Series and Spatial Data (2011, methodology): “For regularity conditions and further detail, we refer to the original work of Davies and Hall (1999), Chan and Wood (2000), Zhu and Stein (2002) and Chan and Wood (2004), which is impressive.”
Simultaneous estimation of the parameters of the Hurst–Kolmogorov stochastic process (2011, methodology): “Besides new estimators are proposed, for example Guerrero and Smith (2005) presented a maximum likelihood based estimator, while Coeurjolly (2008) presented estimators based on convex combinations of sample quantiles of discrete variations of a sample path over a discrete grid of the interval [0,…”
Estimation of time-dependent Hurst exponents with variational smoothing and application to forecasting foreign exchange rates (2017, methodology): “Beside the previously mentioned methods for estimating global Hurst exponents, other ways are possible, such as the convex combination of sample quantiles [14] or the increment ratio statistic [5, 7].”
Modeling stock prices by multifractional Brownian motion: an improved estimation of the pointwise regularity (2013, background): “Finally, a class of consistent estimators based on convex combinations of sample quantiles of discrete variations was proposed by Coeurjolly ( 2008 ), who also derives the almost certain convergence and the asymptotic normality of the estimators.”