A simple sequential outlier detection with several residuals

Outlier detection schemes have been used to identify the unwanted noise and this helps us to obtain underlying valuable signals and predicting the next state of the systems/signals. However, there are few researches on sequential outlier detection in time series although a lot of outlier detection algorithms are developed in off-line systems. In this paper, we focus on the sequential (on-line) outlier detection schemes, that are based on the `delete-replace´ approach. We also demonstrate that three different types of residuals can be used to design the outlier detection scheme to achieve accurate sequential estimation: marginal residual, conditional residual, and contribution.