Hybrid Lee-Carter Model with Adaptive Network of Fuzzy Inference System and Wavelet Functions

Abstract

Mortality studies are essential in determining the health status and demographic composition of a population. The Lee–Carter (LC) modelling framework is extended to incorporate the macroeconomic variables that affect mortality, especially in forecasting. This paper makes several major contributions. First, a new model (LC-WT-ANFIS) employing the adaptive network-based fuzzy inference system (ANFIS) was proposed in conjunction with a nonlinear spectral model of maximum overlapping discrete wavelet transform (MODWT) that includes five mathematical functions, namely, Haar, Daubechies (d4), least square (la8), best localization (bl14), and Coiflet (c6) to enhance the forecasting accuracy of the LC model. Annual mortality data was collected from five countries (Australia, England, France, Japan, and the USA) from 1950 to 2016. Second, we selected gross domestic product (GDP), unemployment rate (UR), and inflation rate (IF) as input values according to correlation and multiple regressions. The input variables in this study were obtained from the World Bank and Datastream. The output variable was collected from the mortality rates in Human Mortality Database. Finally, the LC model’s projected log of death rates was compared with wavelet filters and the traditional LC model. The performance of the proposed model (LC-WT-ANFIS) was evaluated based on mean absolute percentage error (MAPE) and mean error (ME). Results showed that the LC-WT-ANFIS model performed better than the traditional model. Therefore, the proposed forecasting model is capable of projecting mortality rates.