Estimating Spectral Density Functions Robustly

Abstract

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.