This study implements various, maximum overlap, discrete wavelet transform filters to model and forecast the time-dependent mortality index of the Lee-Carter model. The choice of appropriate wavelet filters is essential in effectively capturing the dynamics in a period. This cannot be accomplished by using the ARIMA model alone. In this paper, the ARIMA model is enhanced with the integration of various maximal overlap discrete wavelet transform filters such as the least asymmetric, best-localized, and Coiflet filters. These models are then applied to the mortality data of Australia, England, France, Japan, and USA. The accuracy of the projecting log of death rates of the MODWT-ARIMA model with the aforementioned wavelet filters are assessed using mean absolute error, mean absolute percentage error, and mean absolute scaled error. The MODWT-ARIMA (5,1,0) model with the BL14 filter gives the best fit to the log of death rates data for males, females, and total population, for all five countries studied. Implementing the MODWT leads towards improvement in the performance of the standard framework of the LC model in forecasting mortality rates.
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.
The Lee-Carter (LC) model led to the development of many prominent mortality models. This study aims to modify the generalised linear model (GLM) (Poisson, negative binomial, and binomial) framework of the LC model by incorporating factors that affect mortality into the model. The top three factors which affect the mortality for each of the 14 countries studied were selected using the random forest recursive feature elimination (RF-RFE) method which eliminates the least important factors based on the correlation of the predictors with the log-mortality rate. These selected factors were integrated in the form of additional bilinear variates to the GLM models and compared to their original counterparts. The RF-RFE method is effective in selecting the best determinants of mortality by avoiding multicollinearity among predictor variables. The inclusion of the time-factor modulation based on the factors selected improved the model adequacy significantly. Vast improvement was evident in the Poisson and binomial settings. Furthermore, the modified GLM version fits short-base-period data well. This study shows that the inclusion of exogenous determinants of mortality improves the performance of the model significantly.
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