This thesis presents collaborative research conducted at the Bureau International des Poids et Mesures (BIPM), specifically within its Time Department. The BIPM serves as the international authority on metrology, facilitating global uniformity in measurements and standards. In this framework, the Time Department is specialized in analyzing time differences data, sourced from atomic clocks distributed across laboratories worldwide. These data are optimally combined to establish a stable and precise time-scale, the Universal Coordinate Time (UTC) scale, used as a global time reference. The thesis commences with a comprehensive literature review addressing the current methodologies and their evolution. Thereafter, the study focuses on the implementation and refinement of algorithms for predicting phase error terms.