M-regression spectral estimator for periodic ARMA models. An empirical investigation

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

1 Federal University of Espírito Santo
2 UFMG - Universidade Federal de Minas Gerais = Federal University of Minas Gerais [Belo Horizonte, Brazil]
3 L2S - Laboratoire des signaux et systèmes
4 MIA Paris-Saclay - Mathématiques et Informatique Appliquées

The M-regression estimator has recently been widely used to build spectral estimators in time series models. In this paper, we extend this approach when the data follow a periodic autoregressive moving average (PARMA) process. We introduce an estimator of the parameters based on the classical Whittle estimator. The finite sample size performances of the proposed estimator are analyzed under the scenarios of PARMA processes with and without additive outliers (AO). Under the non-contaminated scenario, our estimator and the maximum Gaussian and Whittle likelihood estimators have similar behaviors. However, in the contaminated case, the two last estimators are severely biased, while the proposed estimator is robust. As a real data application, carbon monoxide (CO) concentrations are analyzed. A PARMA model is fitted and the data are forecasted with the model.

Keywords: Periodic stationarity; PARMA models; Robust estimation; Outliers; Whittle estimation; CO concentration

Domains: Statistics Theory [stat.TH]; Applications [stat.AP]; Atmospheric and Oceanic Physics [physics.ao-ph]

Alessandro José Queiroz Sarnaglia, Valdério Anselmo Reisen, Pascal Bondon, Céline Lévy-Leduc. M-regression spectral estimator for periodic ARMA models. An empirical investigation. Stochastic Environmental Research and Risk Assessment, 2021, 35 (3), pp.653-664. ⟨10.1007/s00477-020-01958-y⟩. ⟨hal-03185742⟩