Nonparametric estimation of the characteristic triplet of a discretely observed Lévy process
By S. Gugushvili. 2008
54 citations recorded by the source corpus.
Given a discrete time sample X 1, … X n from a Lévy process X=(X t ) t≥0 of a finite jump activity, we study the problem of nonparametric estimation of the characteristic triplet (γ, σ2, ρ) corresponding to the process X. Based on Fourier inversion and kernel smoothing, we propose estimators of γ, σ2 and ρ and study their asymptotic behaviour. The obtained results include derivation of upper bounds on the mean square error of the estimators of γ and σ2 and an upper bound on the mean integrated square error of an estimator of ρ.
Subfields: Finance, Management Science and Operations Research, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f7eb9cdff1e50177eab322361a7aee8885bcffbc
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In Finance
- Denis Belomestny
- Richard Nickl
- Johanna Kappus
- Markus Reiß
- Jean Jacod
- V. Todorov
- Yacine Aït-Sahalia
- Markus Bibinger
In Management Science and Operations Research
In Mathematical Physics
Citations in the corpus
- Spectral estimation of the fractional order of a Lévy process (2010, methodology): “A semiparametric estimation problem for Lévy models has recently been considered in Neumann and Reiss (2009) and Gugushvili (2008).”
- Estimation of the characteristics of a Lévy process observed at arbitrary frequency (2010, background): “Not surprisingly, in that case we face a more complicated inference problem leading to a deconvolution-type inverse problem [9, 2, 6].”
- A Donsker Theorem for Lévy Measures (2012, methodology): “This problem was studied in Gugushvili (2009) for Lévy processes with finite jump activity and a Gaussian part, Comte and Genon-Catalot (2010) for a model selection procedure in the finite variation case, or Trabs (2011) for self-decomposable processes.”