Outlier Detection for Multivariate Time Series: A Functional Data Approach ®

Abstract

[Abstract] A method for detecting outlier samples in a multivariate time series dataset is proposed. It is assumed that an outlying series is characterized by having been generated from a different process than those associated with the rest of the series. Each multivariate time series is described by means of an estimator of its quantile cross-spectral density, which is treated as a multivariate functional datum. Then an outlier score is assigned to each series by using functional depths. A broad simulation study shows that the proposed approach is superior to the alternatives suggested in the literature and demonstrates that the consideration of functional data constitutes a critical step. The procedure runs in linear time with respect to both the series length and the number of series, and in quadratic time with respect to the number of dimensions. Two applications concerning financial series and ECG signals highlight the usefulness of the technique.