Time series that contain a trend, a seasonal component and periodically correlated time series are commonly encountered in environmental sciences. A semiparametric three-step method is proposed to analyze such time series. The seasonal component and trend are estimated by means of B-splines, and the Yule–Walker estimates of the time series model coefficient are calculated via the residuals after removing the estimated seasonality and trend. The oracle efficiency of the proposed Yule–Walker type estimators is established. Simulation studies suggest that the performance of the estimators coincide with the theoretical results. The proposed method is applied to the monthly global temperature data provided by the National Space Science and Technology Center.
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