Nonparametric estimation for L\'evy processes from low-frequency observations

By Michael H. Neumann, Markus Reiß. 2007

156 citations recorded by the source corpus.

We suppose that a L\'evy process is observed at discrete time points. A rather general construction of minimum-distance estimators is shown to give consistent estimators of the L\'evy-Khinchine characteristics as the number of observations tends to infinity, keeping the observation distance fixed. For a specific $C^2$-criterion this estimator is rate-optimal. The connection with deconvolution and inverse problems is explained. A key step in the proof is a uniform control on the deviations of the empirical characteristic function on the whole real line.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/65fcc7069fbe7e9b290f765b0ecf068b2dbb3e91

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

In Management Science and Operations Research

Citations in the corpus

Estimation for L\'{e}vy processes from high frequency data within a long time interval (2011, methodology): “(H1) For statistical purposes, this assumption, which was proposed in Neumann and Reiss (2009), has several useful consequences.”
A Donsker Theorem for Lévy Measures (2012, background): “To see this we argue as in Lemma 1 in Giné and Nickl (2009): note that a function of bounded variation is the composition of a 1-Lipschitz function with a monotone function.”
Efficient estimation of integrated volatility in presence of infinite variation jumps (2014, methodology): “Finally, the empirical characteristic function in low frequency setting has been used in [10, 13] and [14] for estimating the diffusion coefficient of a Lévy process, in [7] for nonparametric estimation for a Lévy process which is a sum of a drift, a symmetric stable process and a compound Poisson p”
Statistical inference for time-changed Lévy processes via composite characteristic function estimation (2010, methodology): “This problem is rather challenging and has not been yet given attention in the literature, except for the special case of T (t) ≡ t [see, e.g., Neumann and Reiß (2009) and Comte and Genon-Catalot (2010)].”
Nonparametric estimation for pure jump Lévy processes based on high frequency data. (2009, unknown): “Illustrations of this approach can be found in Watteel and Kulperger (2003), Jongbloed and van der Meulen (2006), Neumann and Reiss (2007), Jongbloed et al. (2005) for the related problem of L´evy-driven Ornstein-Uhlenbeck processes or Comte and Genon-Catalot (2008).”
Nonparametric estimation of the characteristic triplet of a discretely observed Lévy process (2008, background): “lem is referred to as decompounding. Nonparametric estimation of the L´evy measure ν based on low frequency observations from a general L´evy process X was studied in Watteel and Kulperger (2003) and Neumann and Reiß (2007). However, these authors treat the case of estimation of the L´evy measure on”