Statistical analysis and monitoring of time-series panels, with a particular focus on sunspot counts

Quality control refers to the continuous surveillance of a process to detect its potential anomalies and has many applications in a large variety of fields. Typical examples include the supervision of manufactured products in industries or the control of energy production over time. Different methods based on traditional control charts or machine learning approaches can be used for that purpose. Such typical monitoring problems become however much more complicated when the data are non-normally distributed, correlated along time and experience a wide range of deviations that vary in shapes and sizes. In this context, this thesis aims at exploring non-parametric methods to monitor panels of time-series. The proposed control schemes are tailored to cope with the various autocorrelation structures of the data as well as potential missing values and low signal-to-noise ratios. Although general, those methods are applied here to one main particular example related to the sunspot counts, which are at the basis of the International Sunspot Number (ISN), the world reference for modelling long-term solar activity. This index is one of the most intensively used time-series of astrophysics and appears in a large variety of models including those of the Earth climate. The proposed methods are designed to identify early any potential inconsistencies that may compromise the stability and accuracy of the series in the future. Moreover, those methods allow the identification of many deviations in past data, whose corrections will lead to a more precise reconstruction of the ISN.