A local correlation integral method for outlier detection in spatially correlated functional data

This paper proposes a new methodology for detecting outliers in spatially correlated functional data. We use a Local Correlation Integral (LOCI) algorithm substituting the Euclidean distance calculation by the Hilbert space L² distance weighted by the semivariogram, obtaining a weighted dissimilarity metric among the geo-referenced curves, which takes into account the spatial correlation structure. In addition, we also consider the distance proposed in Romano et al. (2020), which optimizes the distance calculation for spatially dependent functional data. A simulation study is conducted to evaluate the performance of the proposed methodology. We analyze the role of a threshold value appearing as an hyperparameter in our approach, and show that our distance weighted by the semivariogram is overall superior to the other types of distances considered in the study. We analyze time series of Land Surface Temperature (LST) data in the region of Andalusia (Spain), detecting significant outliers that would have not been detected using other procedures.