Abstract
This paper discusses decomposition of seasonal time series based on locally weighted regression. With polynomials and trigonometric functions as local regressors a time series is decomposed into unobserved components. The asymptotic behaviour of the proposed estimators are investigated. The focus is on the development of a data-driven procedure. For the selection of bandwidths a mean averaged squared error criterion is used with a bootstrap variance estimator. The selection of the optimal polynomial order is also considered. For the smooth trend-cyclical component also the first derivative, which gives information about instantaneous changes of the trend-cyclical when applied to macro-economic data, is estimated. Application to a German macro-economic time series is presented as illustration. Differences between the proposed method and the other well-known ones based on parametric models are briefly discussed.
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