Calendar effect and in-sample forecasting

A very popular forecasting tool in the actuarial sciences is the so-called chain ladder. Mammen et al. (2015) recently introduced in-sample forecasting, a general forecasting technique applicable in many fields which builds on the continuous chain ladder of Martínez-Miranda et al. (2013). The main aim of this paper is to develop an extended version of the continuous chain ladder which allows for a calendar effect. This extension is of interest not only for actuaries but has many potential applications in economics and other fields. The statistical problem underlying the extended continuous chain ladder is to estimate and forecast a structured nonparametric density. In the theoretical part of the paper, we develop methodology to approach this problem. The usefulness of the methods is illustrated by empirical examples from economics and the actuarial sciences.