Estimating Spectral Density Functions Robustly

• We consider in the following the problem of robust spectral density estimation. Unfortunately, conventional spectral density estimators are not robust in the presence of additive outliers (cf. [18]). In order to get a robust estimate of the spectral density function, it turned out that cleaning the time series in a robust way first and calculating the spectral density function afterwards leads to encouraging results. To meet these needs of cleaning the data we use a robust version of the Kalman filter which was proposed by Ruckdeschel ([26]). Similar ideas were proposed by Martin and Thomson ([18]). Both methods were implemented in R (cf. [23]) and compared by extensive simulation experiments. The competitive method is also applied to real data. As a special practical application we focus on actual heart rate variability measurements of diabetes patients. Key-Words: • robustness; spectral density function; AO-model. AMS Subject Classification: • 62F35, 62M15, 60G35. 42 Bernhard Spangl and Rudolf Dutter Estimating Spectral Density Functions Robustly 43