Optimal estimation of the supremum and occupation times of a self-similar Lévy process

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Abstract

In this paper we present new theoretical results on optimal estimation of certain random quantities based on high frequency observations of a Lévy process. More specifically, we investigate the asymptotic theory for the conditional mean and conditional median estimators of the supremum/infimum of a linear Brownian motion and a strictly stable Lévy process. Another contribution of our article is the conditional mean estimation of the local time and the occupation time of a linear Brownian motion. We demonstrate that the new estimators are considerably more efficient compared to the classical estimators studied in e.g. [6, 14, 29, 30, 38]. Furthermore, we discuss pre-estimation of the parameters of the underly-ing models, which is required for practical implementation of the proposed statistics.

OriginalsprogEngelsk
TidsskriftElectronic Journal of Statistics
Vol/bind16
Nummer1
Sider (fra-til)892-934
Antal sider43
ISSN1935-7524
DOI
StatusUdgivet - jul. 2022

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