Robust Estimation of Power Spectra

Abstract

Summary: Outliers in time series can play havoc with conventional power spectrum density estimation techniques when the spectrum features of interest consist of one or more peaks of relatively low amplitude. Furthermore, the outliers need not be large relative to the scale of the process in order to have considerable impact on the estimate; they only need to be large relative to the scale of the innovations process. Following a tutorial review of the central notions of robustness and the principles guiding conventional spectrum estimation, methods are presented for computing robust spectral densities. These are quite insensitive to such outliers and produce reliable estimates reflecting the structure of the core portion of the data. Two distinct methods are described. Both are based on robust prewhitening and on weighting the resulting residuals. They differ only in the way prewhitening is done: the first method computes the prewhitened values iteratively through a filtering operation; the second fits a robust autoregressive representation to the data by iterated weighted least squares. Each approach can be regarded as the solution to an intuitively appealing minimization problem, where the solution is exact in one case, approximate in the other. Both procedures have proved to be successful over a wide variety of data sets as will be demonstrated with real and simulated data.