Empirical study of robust estimation methods for PAR models with application to the air quality area

Abstract

This paper compares three estimators for periodic autoregressive (PAR) models. The first is the classical periodic Yule-Walker estimator (YWE). The second is a robust version of YWE (RYWE) which uses the robust autocovariance function in the periodic Yule-Walker equations, and the third is the robust least squares estimator (RLSE) based on iterative least squares with robust versions of the original time series. The daily mean particulate matter concentration (PM10) data is used to illustrate the methodologies in a real application, that is, in the Air Quality area.

Keywords:

• Robust estimation
• PAR models
• outliers
• PM10 pollutant

Acknowledgments

The results in this paper are part of the Master thesis of the first author in the PPGEA-UFES under supervision of the second and third authors. The authors gratefully acknowledge partial financial support from FAPES/ES, CAPES/Brazil and CNPq/Brazil. This paper was revised when Prof. Valdério Reisen was visiting CentraleSupélec (01 to 03/2018). This author is indebted to CentraleSupélec for its financial support. The authors are grateful to the Editor and the referee for the time and efforts in providing very constructive and helpful comments that have led to clarify and substantially improve the quality of the paper.