A robust estimation approach for fitting a PARMA model to real data

Alessandro Jose Queiroz Sarnaglia (1) , Valderio Anselmo Reisen (1, 2) , Pascal Bondon (3) , Céline Lévy-Leduc (4)

1 DEST - Departamento de Estatistica
2 Universade Federal Do Espirito Santo
3 L2S - Laboratoire des signaux et systèmes
4 MIA-Paris - Mathématiques et Informatique Appliquées

This paper proposes an estimation approach of the Whittle estimator to fit periodic autoregressive moving average (PARMA) models when the process is contaminated with additive outliers and/or has heavy-tailed noise. It is derived by replacing the ordinary Fourier transform with the non-linear M-regression estimator in the harmonic regression equation that leads to the classical periodogram. A Monte Carlo experiment is conducted to study the finite sample size of the proposed estimator under the scenarios of contaminated and non-contaminated series. The proposed estimation method is applied to fit a PARMA model to the sulfur dioxide (SO2) daily average pollutant concentrations in the city of Vitória (ES), Brazil.

Domaines: Traitement du signal et de l'image [eess.SP]; Statistiques [math.ST]

Alessandro Jose Queiroz Sarnaglia, Valderio Anselmo Reisen, Pascal Bondon, Céline Lévy-Leduc. A robust estimation approach for fitting a PARMA model to real data. 2016 IEEE Statistical Signal Processing Workshop (SSP), Jun 2016, Palma de Mallorca, Spain. 5 p., ⟨10.1109/ssp.2016.7551740⟩. ⟨hal-01560258⟩