An iterative plug-in algorithm for decomposing seasonal time series using the Berlin Method

We propose a fast data-driven procedure for decomposing seasonal time series using the Berlin Method, the software used by the German Federal Statistical Office in this context. Formula of the asymptotic optimal bandwidth h_A is obtained. Meth- ods for estimating the unknowns in h_A are proposed. The algorithm is developed by adapting the well known iterative plug-in idea to time series decomposition. Asymptotic behaviour of the proposal is investigated. Some computational aspects are discussed in detail. Data example show that the proposal works very well in the practice and that data-driven bandwidth selection is a very useful tool to improve the Berlin Method. Deep insights into the iterative plug-in rule are also provided.