Densities, Spectral Densities and Modality

The paper considers the problem of specifying simple adequate density and spectral density functions. In both cases simplicity is measured by the number of local extremes and a taut string method produces candidate functions with increasing modality. Several concepts of approximation are used to decide if a candidate taut string function is adequate with given data or not. Refinements are introduced that improve the local adaptivity of the procedures.