Parametric estimation for subordinators and induced OU processes

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20 Citations (Scopus)

Abstract

Consider a stationary sequence of random variables with infinitely divisible marginal law, characterized by its Lévy density. We analyse the behaviour of a so-called cumulant Mestimator, in case this Lévy density is characterized by a Euclidean (finite dimensional) parameter. Under mild conditions, we prove consistency and asymptotic normality of the estimator. The estimator is considered in the situation where the data are increments of a subordinator as well as the situation where the data consist of a discretely sampled Ornstein-Uhlenbeck (OU) process induced by the subordinator. We illustrate our results for the Gamma-process and the Inverse-Gaussian OU process. For these processes we also explain how the estimator can be computed numerically.

Original languageEnglish
Pages (from-to)825-847
Number of pages23
JournalScandinavian Journal of Statistics
Volume33
Issue number4
DOIs
Publication statusPublished - 1 Dec 2006
Externally publishedYes

Keywords

  • Cumulant
  • Empirical characteristic function
  • Lévy process
  • Self-decomposable distribution
  • Stationary process

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