Hybrid of the Lee-Carter Model with Maximum Overlap Discrete Wavelet Transform Filters in Forecasting Mortality Rates

Nurul Aityqah Yaacob,Sadam Alwadi,Jamil J Jaber,Ibrahim Mohamed,Dharini Pathmanathan

doi:10.3390/math9182295

Nurul Aityqah Yaacob, Sadam Alwadi + Show 3 more

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https://doi.org/10.3390/math9182295

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Abstract

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.

Highlights

Mortality studies are essential in understanding the demographic structure and indicating the health status of a population
This study considered the hybrid of the maximal overlap discrete wavelet transform (MODWT) with the Lee-Carter model to improve the forecast accuracy of the time-dependent mortality index, k(t)
The MODWT is more advantageous than the discrete wavelet transforms (DWT) for mortality modelling

Summary

Introduction

Mortality studies are essential in understanding the demographic structure and indicating the health status of a population. The analysis of mortality and its historical trends enables a country to comprehend its population dynamics and serves as a foundation for formulating economic and social policies [1]. The Lee-Carter (LC) model [2] significantly contributed to the development of various extensions. Currie [4] extended the LC model to a generalized linear model (GLM) framework where the LC model and its extensions were fitted following the GLM framework in the Poisson and binomial settings. Neves et al [5] considered five probability models (Poisson, binomial, negative binomial, Gaussian, and beta) based on the generalized autoregressive score (GAS) model to estimate the LC parameters and forecast mortality rates

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