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

Abstract

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 h _A is obtained. Methods 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 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.

Keywords:

• time series decomposition
• Berlin Method
• local regression
• bandwidth selection
• iterative plug-in

MSC2000 Codes::

• 62G08
• 62G20
• 62-07
• 65Y15

Acknowledgements

This work was partly supported by the Center for International Economics, University of Paderborn. We are very grateful to the Editor and two referees for their useful comments and suggestions, which helped to improve the quality of the paper clearly. The data for the time series CAPE and Hsales are downloaded from the Time Series Data Library. We would like to thank Prof. Rob J. Hyndman, Monash University, for making these data publicly available.