Modeling the number of hidden events subject to observation delay

TL;DR

This paper develops a granular statistical model to predict unobserved past events affected by observation delays, improving accuracy in fields like insurance and disease outbreak modeling.

Contribution

It introduces a novel heterogeneity-aware model for observation delay, incorporating occurrence and calendar effects, enhancing prediction of unreported events.

Findings

Model accurately predicts delayed insurance claims.

Incorporates calendar effects like weekdays and holidays.

Reduces systematic underestimation of event counts.

Abstract

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.