Trend and seasonal decomposition in discrete time

A time series is decomposed into a trend-cyclical plus seasonal component by minimizing the sum of a smoothness and a goodness of fit criterion. The smoothness criterion is such that polynomials (trend-cyclical component) and trigonometric functions (seasonal component) are rated with the ideal value zero. The residual sum of squares serves as goodness of fit criterion. The solution is then decomposed into the two components in a natural way.