Detection of Emergent Anomalous Structure in Functional Data

Motivated by an example arising from digital networks, we propose a novel approach for detecting the emergence of anomalies in functional data. In contrast to classical functional data approaches, which detect anomalies in completely observed curves, the proposed approach seeks to identify anomalies sequentially as each point on the curve is received. The new method, the Functional Anomaly Sequential Test (FAST), captures the common profile of the curves using Principal Differential Analysis and uses a form of CUSUM test to monitor a new functional observation as it emerges. Various theoretical properties of the procedure are derived. The performance of FAST is then assessed on both simulated and telecommunications data.