2014/09/01 by H. Masuda, Hiroki Masuda, Masuda, Hiroki · 5 citations
Economics, Econometrics and Finance · Mathematics · #Applied mathematics #Convergence (economics) #Econometrics #Economics #Estimation theory #FOS: Mathematics #Financial Risk and Volatility Modeling #Focus (optics) #Jump #Likelihood function #Lévy process #Mathematics #Parametric statistics #Statistical physics #Statistics #Statistics Theory (math.ST) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1409.0292
published in arXiv (Cornell University) (Cornell University)
arxiv created 2014/09/01 · openalex publication_date 2014/09/01 · arxiv updated 2014/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The main purpose of this chapter is to present some theoretical aspects of parametric estimation of Lévy processes based on high-frequency sampling, with a focus on infinite activity pure-jump models. Asymptotics for several classes of explicit estimating functions are discussed. In addition to the asymptotic normality at several rates of convergence, a uniform tail-probability estimate for statistical random fields is given. As specific cases, we discuss method of moments for the stable Lévy processes in much greater detail, with briefly mentioning locally stable Lévy processes too. Also discussed is, due to its theoretical importance, a brief review of how the classical likelihood approach works or does not, beyond the fact that the likelihood function is not explicit.