Statistics and Its Interface

Volume 6 (2013)

Number 4

On smoothing estimation for seasonal time series with long cycles

Pages: 435 – 447



Song Xi Chen (Department of Statistics, Iowa State University, Ames, Ia., U.S.A.; Guanghua School of Management and Center for Statistical Science, Peking University, Beijing, China)

Zheng Xu (Department of Biostatistics and Department of Genetics, University of North Carolina, Chapel Hill, N.C., U.S.A.)


We consider a kernel smoothing estimator to the periodic component of seasonal time series which have quite a large periodicity relative to the length of the time series. The estimator is formulated by smoothing the commonly used seasonal-dummy estimator. It combines the neighboring seasonal-dummy estimates of the periodic function so as to reduce the variance of the estimation. We provide some theoretical justifications to the approach as well as simulation evaluations to demonstrate its effectiveness. The proposed approach is used to analyze the return rates of a German electricity price index.


kernel estimator, M-dependent, seasonal-dummy approach

2010 Mathematics Subject Classification

Primary 62G05, 62M10. Secondary 91B84.

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