Detection of outliers in functional time series

A functional depth measures the “centrality” of a functional datum (a function observed over a continuum, for example, a curve, an image) with respect to a given functional dataset. This paper proposes a way to detect outliers in functional time series based on functional depth. Ideally, the depth of a functional outlier should be very low but, when is it low enough to correspond to an outlier? This paper aims to address this question. It uses bootstrap techniques, which take into account the dependence between functional data, to solve this discriminant problem. Several Monte Carlo experiments were designed to explore the performance of the proposed procedure and compare it with some existing methods in the statistical literature related to independent functional data. The proposed methodology was finally used to detect outliers in temperature data and NOx emission data. Results conclude that dependence of data must be taken into account to detect outliers in functional time series. Copyright © 2015 John Wiley & Sons, Ltd.