Empirical regression for trend elimination and smoothing of time series 1,2,3.

The mathematical background of empirical regression its meaning, and its role in a first stage of data evaluation will be sketched. In the second part, applications of empirical regression procedures for time series analysis will be presented, especially for a model-free quantitative description of the trend component in nonstationary time series and for trend elimination with regard to a further spectral, decomposition and spectral characterization of the modified time series.