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Neighbouring prediction for mortality. (English) Zbl 1480.91248

Summary: We propose a new neighbouring prediction model for mortality forecasting. For each mortality rate at age \(x\) in year \(t\), \(m_{x,t}\), we construct an image of neighbourhood mortality data around \(m_{x,t}\), that is, \(\mathcal{E}_{m_{x,t}}(x_1, x_2, s)\), which includes mortality information for ages in \([x-x_1, x+x_2]\), lagging \(k\) years \((1 \leq k \leq s)\). Combined with the deep learning model – convolutional neural network, this framework is able to capture the intricate nonlinear structure in the mortality data: the neighbourhood effect, which can go beyond the directions of period, age, and cohort as in classic mortality models. By performing an extensive empirical analysis on all the 41 countries and regions in the Human Mortality Database, we find that the proposed models achieve superior forecasting performance. This framework can be further enhanced to capture the patterns and interactions between multiple populations.

MSC:

91G05 Actuarial mathematics
68T07 Artificial neural networks and deep learning
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