Identifying influential observations in a time series from the frequency domain point of view

Abstract

This study attempts to explore the influence of observations in a time series or a discrete time signal. The goal is to detect abnormal observations from a frequency domain point of view, while the most of relevant studies have been done from a time domain point of view. The concept of the influence function in the field of robust statistics is borrowed to identify influential observations in a time series. An empirical version of the influence function on the discrete Fourier transform of a time series is designed and subsequently a statistic is proposed to identify influential observations of a time series from the frequency domain point of view. Though the proposed statistic is simple enough to be calculated with simple arithmetic operations, case studies show that the proposed method is capable of identifying influential or abnormal observations of a time series. By identifying influential or abnormal observations, we would be able to gain a better understanding of the nature of a time series and to control possible future influential observations.