Autoregressive model with double Pareto distributed noise

• Autorzy: Woszczek Hubert Piotr , Wyłomańska Agnieszka

Identyfikatory

DOI

10.14708/ma.v51i1.7221

Warianty tytułu

PL

Model autoregresyjny z szumem o podwójnym rozkładzie Pareto

• Języki publikacji: EN

Abstrakty

EN

Time series models are a popular tool commonly used to describe time-varying phenomena. One of the most popular models is the Gaussian AR. However, when the data have outlier observations with "large" values, Gaussian models are not a good choice. We therefore abandon the assumption of normality of the data distribution and propose the AR model based on the double Pareto distribution. We introduce the estimators of the model's parameters, obtained by the maximum likelihood method. For this purpose, we use the Maclaurin series expansion and the Chebyshev polynomials expansion of the likelihood function. We compare the results with the Yule-Walker estimator in the finite variance case and with the modified Yule-Walker estimator in the infinite variance case. The accuracy of the results obtained was checked by Monte Carlo simulations.

PL

Modele szeregów czasowych to popularne narzędzie powszechnie stosowane do modelowania zjawisk zmiennych w czasie. Najpopularniejszym modelem jest gaussowski model AR, który jest stacjonarny. Jednak gdy w danych występują obserwacje odstające o „dużych“ wartościach, modele gaussowskie nie są odpowiednim narzędziem do ich modelowania. Odchodzimy zatem od założenia o normalności rozkładu danych i proponujemy model AR oparty na podwójnym rozkładzie Pareto. Przedstawiamy estymatory parametrów modelu, uzyskane metodą największej wiarygodności. W tym celu wykorzystujemy rozwinięcie funkcji warogodności w szereg zmodyfikowanym estymatorem Yule-Walkera w przypadku nieskończonej wariancji. Poprwaność otrzymanych wyników została sprawdzona za pomocą symulacji Monte Carlo.

Słowa kluczowe

EN

autoregressive model; double Pareto distribution; maximum likelihood estimation; Monte Carlo simulations

PL

model autoregresyjny; podwójny rozkład Pareto; symulacje MC

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Mathematica Applicanda
• Rocznik: 2023
• Tom: Vol. 51, no. 1
• Strony: 121--141
• Opis fizyczny: Bibliogr. 30 poz., wykr.

Twórcy

autor

Woszczek Hubert Piotr

• student Wrocław University of Science and Technology: Wrocław, PL

• https://orcid.org/0009-0006-2911-453X

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

Bibliografia

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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).