Linear fractional stable motion: A wavelet estimator of the α parameter

Antoine Ayache and Julien Hamonier

Statistics & Probability Letters, 2012, vol. 82, issue 8, 1569-1575

Abstract: Linear fractional stable motion, denoted by {XH,α(t)}t∈R, is one of the most classical stable processes; it depends on two parameters H∈(0,1) and α∈(0,2). The parameter H characterizes the self-similarity property of {XH,α(t)}t∈R while the parameter α governs the tail heaviness of its finite dimensional distributions; throughout our article we assume that the latter distributions are symmetric, that H>1/α and that H is known. We show that, on the interval [0,1], the asymptotic behavior of the maximum, at a given scale j, of absolute values of the wavelet coefficients of {XH,α(t)}t∈R, is of the same order as 2−j(H−1/α); then we derive from this result a strongly consistent (i.e. almost surely convergent) statistical estimator for the parameter α.

Keywords: Stable stochastic processes; Statistical inference; Wavelet coefficients; Hölder regularity (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spl.2012.04.005

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