TY - JOUR

T1 - Mortality forecasting using factor models

T2 - Time-varying or time-invariant factor loadings?

AU - He, Lingyu

AU - Huang, Fei

AU - Shi, Jianjie

AU - Yang, Yanrong

N1 - Publisher Copyright:
© 2021 Elsevier B.V.

PY - 2021/5

Y1 - 2021/5

N2 - Many existing mortality models follow the framework of classical factor models, such as the Lee–Carter model and its variants. Latent common factors in factor models are defined as time-related mortality indices (such as κt in the Lee–Carter model). Factor loadings, which capture the linear relationship between age variables and latent common factors (such as βx in the Lee–Carter model), are assumed to be time-invariant in the classical framework. This assumption is usually too restrictive in reality as mortality datasets typically span a long period of time. Driving forces such as medical improvement of certain diseases, environmental changes and technological progress may significantly influence the relationship of different variables. In this paper, we first develop a factor model with time-varying factor loadings (time-varying factor model) as an extension of the classical factor model for mortality modelling. Two forecasting methods to extrapolate the factor loadings, the local regression method and the naive method, are proposed for the time-varying factor model. From the empirical data analysis, we find that the new model can capture the empirical feature of time-varying factor loadings and improve mortality forecasting over different horizons and countries. Further, we propose a novel approach based on change point analysis to estimate the optimal ‘boundary’ between short-term and long-term forecasting, which is favoured by the local linear regression and naive method, respectively. Additionally, simulation studies are provided to show the performance of the time-varying factor model under various scenarios.

AB - Many existing mortality models follow the framework of classical factor models, such as the Lee–Carter model and its variants. Latent common factors in factor models are defined as time-related mortality indices (such as κt in the Lee–Carter model). Factor loadings, which capture the linear relationship between age variables and latent common factors (such as βx in the Lee–Carter model), are assumed to be time-invariant in the classical framework. This assumption is usually too restrictive in reality as mortality datasets typically span a long period of time. Driving forces such as medical improvement of certain diseases, environmental changes and technological progress may significantly influence the relationship of different variables. In this paper, we first develop a factor model with time-varying factor loadings (time-varying factor model) as an extension of the classical factor model for mortality modelling. Two forecasting methods to extrapolate the factor loadings, the local regression method and the naive method, are proposed for the time-varying factor model. From the empirical data analysis, we find that the new model can capture the empirical feature of time-varying factor loadings and improve mortality forecasting over different horizons and countries. Further, we propose a novel approach based on change point analysis to estimate the optimal ‘boundary’ between short-term and long-term forecasting, which is favoured by the local linear regression and naive method, respectively. Additionally, simulation studies are provided to show the performance of the time-varying factor model under various scenarios.

KW - Lee–Carter model

KW - Long-term forecasting

KW - Optimal ‘boundary’ estimation

KW - Short-term forecasting

KW - Time-varying factor model

UR - http://www.scopus.com/inward/record.url?scp=85100752222&partnerID=8YFLogxK

U2 - 10.1016/j.insmatheco.2021.01.006

DO - 10.1016/j.insmatheco.2021.01.006

M3 - Article

SN - 0167-6687

VL - 98

SP - 14

EP - 34

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

ER -