Linear fractional stable motion: A wavelet estimator of the \(\alpha\) parameter

DOI10.1016/j.spl.2012.04.005zbMath1456.62177arXiv1302.1674OpenAlexW2060521551MaRDI QIDQ449019

Julien Hamonier, Antoine Ayache

Publication date: 11 September 2012

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.1674

zbMATH Keywords

statistical inferenceHölder regularitywavelet coefficientsstable stochastic processes

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Fractional processes, including fractional Brownian motion (60G22) Point estimation (62F10)

Related Items (8)

A minimal contrast estimator for the linear fractional stable motion ⋮ Estimation of mixed fractional stable processes using high-frequency data ⋮ Linear multifractional stable motion: wavelet estimation of \(H(\cdot)\) and \(\alpha\) parameters ⋮ Estimation of the linear fractional stable motion ⋮ On limit theory for functionals of stationary increments Lévy driven moving averages ⋮ Power variations for fractional type infinitely divisible random fields ⋮ Series representation of jointly \(S \alpha S\) distribution via symmetric covariations ⋮ Scaling properties of the empirical structure function of linear fractional stable motion and estimation of its parameters

Cites Work

• Stochastic integral representation and properties of the wavelet coefficients of linear fractional stable motion
• Estimation of the self-similarity parameter in linear fractional stable motion.
• Bounds for the covariance of functions of infinite variance stable random variables with applications to central limit theorems and wavelet-based estimation
• Sample path properties of ergodic self-similar processes
• Asymptotic self‐similarity and wavelet estimation for long‐range dependent fractional autoregressive integrated moving average time series with stable innovations
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