Time series outlier detection and imputation

This paper proposed the combination of two statistical techniques for the detection and imputation of outliers in time series data. An autoregressive integrated moving average with exogenous inputs (ARIMAX) model is used to extract the characteristics of the time series and to find the residuals. The outliers are detected by performing hypothesis testing on the extrema of the residuals and the anomalous data are imputed using another ARIMAX model. The process is performed in an iterative way because at the beginning the process, the residuals are contaminated by the anomalies and therefore, the ARIMAX model needs to be re-learned on "cleaner" data at every step. We test the algorithm using both synthetic and real data sets and we present the analysis and comments on those results.