A Hybrid Nonparametric Framework for Outlier Detection in Functional Time Series

Outlier detection in functional time series is challenging due to temporal dependence and the simultaneous presence of magnitude, shape, and partial anomalies. Existing methods often assume independence or rely on model based approaches, such as the Standard Smoothed Bootstrap on Residuals (SmBoR), which may not work well if the model is misspecified. Model free alternatives, based on the moving block bootstrap, improve robustness but may detect only a limited number of magnitude anomalies. This work proposes a fully model free pipeline with two components. First, the Directional Outlyingness (DirOut) framework is extended by recalibrating its cutoff via an outlier detection procedure based on the moving block bootstratp (MBBo), improving the detection of shape and partial outliers while controlling false positives. Second, a Sliding Window Functional Boxplot (SWOD) is used to focus on local temporal neighborhoods and detect magnitude anomalies that other methods may miss. Simulations show that SWOD has high detection rates for magnitude outliers, while MBBo calibrated DirOut achieves almost perfect detection for shape and partial anomalies, outperforming SmBoR. The method is also tested on a real temperature dataset, showing its practical usefulness.