Abstract
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 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. 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 concentrations are analyzed. A PARMA model is fitted and the data are forecasted with the model.
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Acknowledgements
The authors would like to thank the agencies CNPq, CAPES and FAVES, Brazil and CNRS and CentraleSupélec, France for their financial support. This research was also partially supported by DATAIA Convergence Institute as part of the “Programme d’Investissement d’Avenir, (ANR17-CONV-0003) operated by CentraleSupélec”, and by the iCODE Institute, research project of the IDEX Paris-Saclay, and by the Hadamard Mathematics LabEx (LMH) through the grant number ANR-11-LABX-0056-LMH in the “Programme d’Investissement d’Avenir”. The authors also thank the referees and the editor for their valuable suggestions which have contributed significantly for the improvement of the paper.
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Sarnaglia, A.J.Q., Reisen, V.A., Bondon, P. et al. M-regression spectral estimator for periodic ARMA models. An empirical investigation. Stoch Environ Res Risk Assess 35, 653–664 (2021). https://doi.org/10.1007/s00477-020-01958-y
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DOI: https://doi.org/10.1007/s00477-020-01958-y