Real-time monitoring of functional data

With the development of data acquisition technologies, huge amounts of data, which are apt to be modeled as functional data, are now generated. In this setting, standard profile monitoring methods aim to assess the stability over time of a completely observed functional quality characteristic. However, in some practical situations, assessing the presence of assignable causes is of great interest even when the functional quality characteristic is not completely observed yet, that is, to monitor the process state in realtime. To this aim, we propose a new method, referred to as functional real-time monitoring (FRTM), that is able to account for both phase and amplitude variation through the following steps: (i) registration, (ii) dimensionality reduction, and (iii) monitoring of a partially observed functional quality characteristic. An extensive Monte Carlo simulation study quantifies the performance of FRTM relative to three competing methods. Finally, a case study addresses the real-time monitoring of household daily electricity demand FRTM is implemented in the R package funcharts, available CRAN.