Least squares estimator of fractional Ornstein-Uhlenbeck processes with periodic mean

Salwa Bajja, Khalifa Es-Sebaiy*, Lauri Viitasaari

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

15 Citations (Scopus)

Abstract

We first study the drift parameter estimation of the fractional Ornstein-Uhlenbeck process (fOU) with periodic mean for every 12<H<1. More precisely, we extend the consistency proved in Dehling et al. (2016) for 12<H<34 to the strong consistency for any 12<H<1 on the one hand, and on the other, we also discuss the asymptotic normality given in Dehling et al. (2016). In the second main part of the paper, we study the strong consistency and the asymptotic normality of the fOU of the second kind with periodic mean for any 12<H<1.

Original languageEnglish
Pages (from-to)608-622
Number of pages15
JournalJOURNAL OF THE KOREAN STATISTICAL SOCIETY
Volume46
Issue number4
DOIs
Publication statusPublished - 2017
MoE publication typeA1 Journal article-refereed

Keywords

  • Fractional Ornstein-Uhlenbeck processes
  • Least squares estimator
  • Malliavin calculus

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