Time series modeling and analysis is central to most financial and econometric data modeling. With increased globalization in trade, commerce and finance, national variables like gross domestic productivity (GDP) and unemployment rate, market variables like indices and stock prices and global variables like commodity prices are more tightly coupled than ever before. This translates to the use of multivariate or vector time series models and algorithms in analyzing and understanding the relationships that these variables share with each other. While robustness and time series modeling have been vastly researched individually in the past, application of robust methods to estimate time series models is still quite open. The central goal of this thesis is the study of the S-estimator, a robust estimator, applied to some simple vector and nonlinear time series models. In each case, we will look at the important aspect of stationarity of the model and analyze the asymptotic behavior of the S-estimator.