A Review of Outlier Detection and Robust Estimation Methods for High Dimensional Time Series Data

Diagnostic procedures for finding outliers in high dimensional multivariate time series and robust estimation methods for these data are reviewed. First, methods for searching for outliers assuming that the data have been generated by a Dynamic Factor Model are presented. Then, other existing methods for detecting different types of multivariate time series outliers are analyzed. They include identifying outlying series and, also, looking for segments, or periods of time, where the series have unusual dynamics. Second, robust estimation methods are considered. Dynamic Principal Components, as a very general procedure to estimate the dynamic in a high dimensional data set, is introduced and different types of robust estimation of these components are reviewed. Dynamic Principal Components can be applied for robust estimation of Generalized Dynamic Factor models and some results are given. Finally, other methods proposed for robust estimation of high dimensional VAR models and other multivariate time series problems are also briefly discussed.