Geodesic
Autoregressive model with double Pareto distributed noise
Mathematica Applicanda, Tome 51 (2023) no. 1, pp. 121-141.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

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.
DOI : 10.14708/ma.v51i1.7221
Classification : 60E05, 60G10
Mots-clés : autoregressive model, double Pareto distribution, maximum likelihood estimation, Monte Carlo simulations 
@article{10_14708_ma_v51i1_7221,
     author = {Hubert Piotr Woszczek and Agnieszka Wy{\l}oma\'nska},
     title = {Autoregressive model with double {Pareto} distributed noise},
     journal = {Mathematica Applicanda},
     pages = { 121--141},
     publisher = {mathdoc},
     volume = {51},
     number = {1},
     year = {2023},
     doi = {10.14708/ma.v51i1.7221},
     language = {pl},
     url = {http://geodesic.mathdoc.fr/articles/10.14708/ma.v51i1.7221/}
}
TY  - JOUR
AU  - Hubert Piotr Woszczek
AU  - Agnieszka Wyłomańska
TI  - Autoregressive model with double Pareto distributed noise
JO  - Mathematica Applicanda
PY  - 2023
SP  -  121
EP  - 141
VL  - 51
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.14708/ma.v51i1.7221/
DO  - 10.14708/ma.v51i1.7221
LA  - pl
ID  - 10_14708_ma_v51i1_7221
ER  - 
%0 Journal Article
%A Hubert Piotr Woszczek
%A Agnieszka Wyłomańska
%T Autoregressive model with double Pareto distributed noise
%J Mathematica Applicanda
%D 2023
%P  121-141
%V 51
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.14708/ma.v51i1.7221/
%R 10.14708/ma.v51i1.7221
%G pl
%F 10_14708_ma_v51i1_7221
Hubert Piotr Woszczek; Agnieszka Wyłomańska. Autoregressive model with double Pareto distributed noise. Mathematica Applicanda, Tome 51 (2023) no. 1, pp.  121-141. doi : 10.14708/ma.v51i1.7221. http://geodesic.mathdoc.fr/articles/10.14708/ma.v51i1.7221/

Cité par Sources :