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2019 | 47 | 2 |
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Fractional lower order covariance based-estimator for Ornstein-Uhlenbeck process with stable distribution

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Języki publikacji
EN
Abstrakty
PL
The Ornstein-Uhlenbeck model is one of the most popular stochastic processes. It has found many interesting applications including physical phenomena. However, for many real data, the classical Ornstein-Uhlenbeck process cannot be applied. It is related to the fact that for many phenomena the vectors of observations exhibit so-called heavy-tailed behaviour. In such cases, the modifications of the classical models need to be used. In this paper, we analyze the Ornstein-Uhlenbeck process based on stable distribution. This distribution is one of the most classical members of the heavy-tailed class of distributions. In the literature, one can find various applications of stable processes. However, the heavy-tailed property implies that the classical methods of estimation and statistical investigation cannot be applied. In this paper, we propose a new method of estimation of stable Ornstein-Uhlenbeck process. This technique is based on the alternative measure of dependence, called fractional lower order covariance, which replaces the classical covariance for infinite-variance distribution. The proposed research is a continuation of the authors' previous studies, where the measure called covariation was proposed as the base for the estimation technique. We introduce the stable Ornstein-Uhlenbeck process and remind its main properties. In the main part, we define the new estimator of the of the parameters for discrete representation of Ornstein-Uhlenbeck process. Its effectiveness is checked by Monte Carlo simulations.
Słowa kluczowe
PL
 
EN
 
Rocznik
Tom
47
Numer
2
Opis fizyczny
Daty
wydano
2019
online
2019-10-05
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ojs-doi-10_14708_ma_v47i2_6506
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