Statistical inference for generalized Ornstein-Uhlenbeck processes

2015/03/11 by Denis Belomestny, Belomestny, Denis, Vladimir Panov +1
Mathematics · #60G51 #62F12 #62M05 #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Probability (math.PR) #math.PR #msc:60G51 #msc:62F12 #msc:62M05 #stat.ME

paper · pdf · doi:10.48550/arxiv.1503.03381

32 pages. arXiv admin note: text overlap with arXiv:1312.4731

arxiv created 2015/03/11 · arxiv updated 2015/03/12

Abstract

In this paper, we consider the problem of statistical inference for generalized Ornstein-Uhlenbeck processes of the type X_t = e^-ξ_t ( X₀ + ∫₀^t e^ξ_u- d u ), where \(ξ_s\) is a Lévy process. Our primal goal is to estimate the characteristics of the Lévy process \(ξ\) from the low-frequency observations of the process \(X\). We present a novel approach towards estimating the Lévy triplet of \(ξ,\) which is based on the Mellin transform technique. It is shown that the resulting estimates attain optimal minimax convergence rates. The suggested algorithms are illustrated by numerical simulations.

Citations

• Statistical inference for exponential functionals of Lévy processes

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