Functional depth measures in the context of functional time series and application to outlier detection

A. Elías Fernández

Functional depth measures have long been a cornerstone of the analysis of independent functional data. However, their extension to time-dependent functional data remains relatively unexplored. In this work, we develop a framework that leverages functional depth measures for functional time series to capture temporal dynamics and identify abnormal periods. Specifically, we consider sequences of curves observed over time and show that depth-based representations can retain and summarise key temporal dependence structures. Building on this idea, we propose a methodology for detecting outlying curves that accounts for both their magnitude and shape, as well as their temporal evolution. We apply the approach to the electricity market, where bids are represented via their price and volume distributions rather than stepwise supply curves. Modelling these distributions as a functional time series enables the detection of atypical market behaviour and potential strategic actions.

Keywords: Functional time series, Outlier detection, Depth measures, Energy market

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