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An iterative plug-in algorithm for nonparametric modelling of seasonal time series

This paper focuses on developing a new data-driven procedure for decomposing seasonal time series based on local regression. Formula of the asymptotic optimal bandwidth hA in the current context is given. Methods for estimating the unknowns in hA are investigated. A data-driven algorithm for decomposing seasonal time series is proposed based on the iterative plug-in idea introduced by Gasser et al. (1991). Asymptotic behaviour of this algorithm is investigated. Some computational aspects are discussed in detail. Practical performance of the proposed algorithm is illustrated by simulated and data examples. The results here also provide some insights into the iterative plug-in idea.