Trend-seasonal decomposition of time series as whittaker-henderson graduation

Abstract

The diagnostic and essentially modelfree seasonal adjustment (SA) procedures of BAYSEA by AKAIKE and of SCHLICHT-PAULY are generalized, in particular by admitting arbitrary and data-dependent weights. This admits iterative analyses such as nonlinear robustification, or minimization of the relative rather than of the absolute errors. One step of these methods rests upon the rather well-known and flexible WHITTAKER-HENDERSON graduation. The uniqueness of its minimizing solution is proved for a given set of decomposition parameters. Quick and easy but high-quality graphical representations are produced by the available packages even on PCs. They serve as important checks in the fast iterative trial and error fitting process of the trend-season decompositions produced.Qualitative as well as quantitative criteria of the fit can be checked. Artefacts, the typical defect of model misspecifications, are efficiently controlled. The tools guarantee the superiority of this type of exploratory approaches over tentative model-based descriptions.

However, it is also pointed out that numerical cancellation may hamper those SA-procedures which use sucessive differences. They are therefore numerically inferior compared to, e.g. the analoguous spline approximations. Various applications, such as prediction are briefly explained. The method is compared in short with other modelfree SA-methods like X 11 and SABL. Reproduction properties, equivariances, outlier resistance, projection aspects, e.g. are indicated

Keywords:

• Descriptive seasonal adjustment
• trend-seasonal decomposition
• diagnostic modelling
• global smoothing
• graphical checks
• robustification