Inférence fondée sur la vraisemblance pour des modèles de records

In a time series {Xt,t≥1}, Xj is said to be an upper record if Xj>max⁡{X1,…,Xj−1}. Some popular models for records are the Yang-Nevzorov and the Linear Drift models. In this note, we introduce for these models the joint likelihood of the record sequence and the indicators of their occurrence. This likelihood can then be used to obtain estimators of the unknown parameters in the models. It can also be used to derive inferential procedures associated with the selection of a proper model for such data.