Applications to Time Series Analysis: Robust Spectrum Estimation
Georgy L. Shevlyakov, Hannu Oja · Wiley series in probability and statistics · 2016
Conventional methods of power spectrum estimation are very sensitive to the presence of outliers in the data; thus generally the issues of robustness are of vital importance within this area of statistics of random processes. This chapter considers various robust versions of the conventional methods of power spectra estimation. It is found that the best robust estimates of power spectrum are based on robust highly efficient estimates of autocovariances. Several open problems for future research are formulated. The chapter proposes a contamination model dubbed as a disorder contamination describing the violations of the thin structure of a random process, when an autoregressive (AR)-process is shortly changed for another and then it returns to the previous state. The chapter applies the robust analogs of the discrete Fourier transform (DFT) as well as the highly robust and efficient estimates of scale and correlation to the classical nonparametric estimation of power spectrum.