Identification of the structure break point for data with changing variance

• Autorzy: Witulska Justyna , Wyłomańska Agnieszka

Identyfikatory

DOI

10.14708/ma.v50i1.7155

Warianty tytułu

PL

Identyfikacja punktu zmiany reżimu dla niezależnych danych o zmiennej wariancji

• Języki publikacji: EN

Abstrakty

EN

In this paper, we discuss the problem of the structure break point detection for data with changing variance. Considering the limitations and advantages of five well-known techniques, we propose a hybrid algorithm dedicated to the considered problem. The new method enables us to detect break point, even if the data exhibit non-Gaussian characteristics and the small differences between variances in separate segments occur. The efficiency is verified for simulated data from three general classes of distributions, namely platykurtic, leptokurtic and mesokurtic classes represented here by Gaussian, Laplace, Student's t, and generalized Gaussian distributions. The simulation study is supported by real data analysis.

PL

W artykule omówiono problem detekcji punktu zmiany reżimu dla danych o zmiennej wariancji. Uwzględniając ograniczenia i zalety pięciu znanych technik, zaproponowano hybrydowe podejscie dla omawianego problemu. Nowa metoda umożliwia wykrycie punktu zmiany, nawet jeśli dane wykazują charakterystykę niegaussowską i występują niewielkie różnice pomiędzy wariancjami w poszczególnych segmentach. Skuteczność metody jest weryfikowana dla danych symulowanych pochodzących z trzech ogólnych klas rozkładów, mianowicie platykurtycznych, leptokurtycznych oraz mezokurtycznych reprezentowanych tutaj przez rozkład normalny, Laplace'a, t-Studenta oraz uogólniony rozkład normalny. Badania symulacyjne poparte są analizą danych rzeczywistych.

Słowa kluczowe

EN

changing variance; change point; Monte Carlo simulation; real data analysis

PL

zmienna wariancja; zmiana reżimu; symulacje Monte Carlo; analiza danych rzeczywistych

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Mathematica Applicanda
• Rocznik: 2022
• Tom: Vol. 50, no. 1
• Strony: 65--106
• Opis fizyczny: Bibliogr. 84 poz., rys., tab., wykr.

Twórcy

autor

Witulska Justyna

• studentka Wrocław University of Science and Technology Wybrzeze Wyspianskiego 27, 50-370 Wrocław, Poland

• https://orcid.org/0000-0003-4351-0783

autor

Wyłomańska Agnieszka

• Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, Wrocław 50-370

• https://orcid.org/0000-0001-9750-1351

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Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).