  This paper considers the problem of predicting the number of events that have
occurred in the past, but which are not yet observed due to a delay. Such
delayed events are relevant in predicting the future cost of warranties,
pricing maintenance contracts, determining the number of unreported claims in
insurance and in modeling the outbreak of diseases. Disregarding these
unobserved events results in a systematic underestimation of the event
occurrence process. Our approach puts emphasis on modeling the time between the
occurrence and observation of the event, the so-called observation delay. We
propose a granular model for the heterogeneity in this observation delay based
on the occurrence day of the event and on calendar day effects in the
observation process, such as weekday and holiday effects. We illustrate this
approach on a European general liability insurance data set where the
occurrence of an accident is reported to the insurer with delay.
