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Robust estimation of periodic autoregressive processes in the presence of additive outliers

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  • Sarnaglia, A.J.Q.
  • Reisen, V.A.
  • Lévy-Leduc, C.

Abstract

This paper suggests a robust estimation procedure for the parameters of the periodic AR (PAR) models when the data contains additive outliers. The proposed robust methodology is an extension of the robust scale and covariance functions given in, respectively, Rousseeuw and Croux (1993) [28], and Ma and Genton (2000) [23] to accommodate periodicity. These periodic robust functions are used in the Yule-Walker equations to obtain robust parameter estimates. The asymptotic central limit theorems of the estimators are established, and an extensive Monte Carlo experiment is conducted to evaluate the performance of the robust methodology for periodic time series with finite sample sizes. The quarterly Fraser River data was used as an example of application of the proposed robust methodology. All the results presented here give strong motivation to use the methodology in practical situations in which periodically correlated time series contain additive outliers.

Suggested Citation

  • Sarnaglia, A.J.Q. & Reisen, V.A. & Lévy-Leduc, C., 2010. "Robust estimation of periodic autoregressive processes in the presence of additive outliers," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2168-2183, October.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:9:p:2168-2183
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    1. Reisen, Valdério Anselmo & Monte, Edson Zambon & da Conceição Franco, Glaura & Sgrancio, Adriano Marcio & Molinares, Fábio Alexander Fajardo & Bondon, Pascal & Ziegelmann, Flávio Augusto & Abraham, Bo, 2018. "Robust estimation of fractional seasonal processes: Modeling and forecasting daily average SO2 concentrations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 146(C), pages 27-43.
    2. Francesco Battaglia & Domenico Cucina & Manuel Rizzo, 2020. "Detection and estimation of additive outliers in seasonal time series," Computational Statistics, Springer, vol. 35(3), pages 1393-1409, September.
    3. PEREAU Jean-Christophe & URSU Eugen, 2015. "Application of periodic autoregressive process to the modeling of the Garonne river flows," Cahiers du GREThA (2007-2019) 2015-14, Groupe de Recherche en Economie Théorique et Appliquée (GREThA).

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