High Breakdown Methods of Time Series Analysis

Abstract

SUMMARY A robust form of the discrete Fourier transform is developed that can handle large amounts of contamination and patchy outliers. We use robust regression to fit a sine and cosine coefficient at each Fourier frequency, and these coefficients are then inverse Fourier transformed to give a filtered version of the data. The filtered series can then be analysed with conventional methods. The limiting breakdown bound of the filter is 50%. Other properties of the filter are also given. The performance of our method is compared by a Monte Carlo study with that of a data cleaner of Martin and Thomson. A comparison of the methods, including an outlier detection procedure, is also done by using a real data set with patchy outliers.