- Tytuł:
-
Fractional lower order covariance based-estimator for Ornstein-Uhlenbeck process with stable distribution
Estymator bazujący na ułamkowych momentach dla procesu Ornsteina-Uhlenbecka z rozkładem stabilnym - Autorzy:
-
Kruczek, Piotr
Żuławiński, Wojciech
Pagacz, Patrycja
Wyłomańska, Agnieszka - Powiązania:
- https://bibliotekanauki.pl/articles/953445.pdf
- Data publikacji:
- 2019
- Wydawca:
- Polskie Towarzystwo Matematyczne
- Tematy:
-
ornstein-uhlenbeck process
floc
estimation
stable distribution - Opis:
- 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.
- Źródło:
-
Mathematica Applicanda; 2019, 47, 2
1730-2668
2299-4009 - Pojawia się w:
- Mathematica Applicanda
- Dostawca treści:
- Biblioteka Nauki
Artykuł