Detecting Outliers in High-Dimensional Time Series by Dynamic Factor Models

A procedure to detect outliers in a large collection of time series is presented. The high-dimensional setting is handled by assuming that the time series have been generated by a dynamic factor model and that outliers can appear either in the latent factors or in the idiosyncratic noise. The factor outliers affect all or many of the time series, whereas the idiosyncratic outliers affect only a few, or just one, of the observed time series. These two types of outliers can be fairly well detected by projecting the series on the factor and idiosyncratic spaces constructed from robust estimates of the factor loading matrix. We propose an efficient procedure based on these linear transformations for detecting outliers. Its behavior is illustrated with simulations and the analysis of a real data example.