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Title: Evolution outliers in high dimensional functional time series Authors:  Antonio Elias - Universidad de Malaga (Spain)
Salvador Pineda - OASYS Group Universidad de Malaga (Spain)
Juan Miguel Morales - OASYS Group Universidad de Malaga (Spain)
Antonio Elias - Universidad de Malaga (Spain) [presenting]
Abstract: Functional depth measures have been a cornerstone to build outlier detection methods for samples of independent and identically distributed curves. We aim to use this concept to extract information of the temporal dependency of Functional Time Series (FTS) that are sets of sample curves indexed in time. More precisely, we focus on High Dimensional Functional Time Series (HDFTS) that terms the situation when several FTS are under analysis. In this scenario, we use functional depth measures to detect evolution outliers that are individual FTS with abnormal time dependency patterns. The performance of our method is tested by simulating HDTS with mixtures of different time dependency structures, namely, time-independent samples, functional dynamic factor models, functional autoregressive models (FAR), functional moving average models (FMA), functional autoregressive and moving average models (FARMA) and functional autoregressive models with seasonality (SFAR). This methodology is motivated by the analysis of data gathered by Energy Smart Metering Infrastructures. They are a multitude of meters that record numerous features such as energy consumption, household circuit voltage, or photo-voltaic energy generation during long time periods at a very high-frequency rate. In this context, we show our HDFTS outlier detection approach with actual smart meters data related to photovoltaic energy generation and circuit voltage records.