Statistics and Its Interface

Volume 10 (2017)

Number 1

Semiparametric analysis for environmental time series

Pages: 71 – 79



Lin Tang (Department of Mathematics and Statistics, University of Toledo, Ohio, U.S.A.)

Qin Shao (Department of Mathematics and Statistics, University of Toledo, Ohio, U.S.A.)


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.


periodic autoregressive time series, partially linear models, Yule–Walker estimators, B-splines, oracle efficiency, confidence band, trend, seasonality

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Published 27 September 2016