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 procedure used, e.g. by the German Federal Statistical Office in this context. The formula of the asymptotic optimal bandwidth hA is obtained. Methods for estimating the unknowns in hA 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 examples show that the proposal works very well in practice and that data-driven bandwidth selection offers new possibilities to improve the Berlin Method. Deep insights into the iterative plug-in rule are also provided.