Time series: theory and methods
Time series: theory and methods
Outliers and financial time series modelling: a cautionary note
Selected papers of the MSSA/IMACS 10th biennial conference on Modelling and simulation
Time Series Analysis, Forecasting and Control
Time Series Analysis, Forecasting and Control
New Introduction to Multiple Time Series Analysis
New Introduction to Multiple Time Series Analysis
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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.