This book deals with the methods of detection, and identification of outliers in time series data in the frequency domain. It also discusses the method of analysis that would be insensitive to outliers. The author uses some robust regression method to fit sine and cosine coefficients at each Fourier frequency assuming additive outlier (AO) and multiplicative outliers (MO) respectively to obtain discrete Fourier transform for removing outliers from time series data. The parameters of the contaminated series were estimated using the maximum likelihood (ML) method and the statistical properties of the derived estimates were investigated. Two algorithms were proposed for detection and accommodation of aberrant observations in the frequency domain while modified test statistic using a more robust estimate that is resistant to outlier were also developed to test each observation for discordance. A new filtering method of accommodating outliers was also suggested and the performance of various accommodation techniques was determined in respect of the fixed and dynamic models.Real life and simulated data were used to illustrate the techniques.