Evaluation of the Product Ratio Coherent Model in Forecasting Mortality Rates and Life Expectancy at Births by States

Coherent mortality forecasting models have recently received increasing attention particularly in their application to sub-populations. The advantage of coherent models over independent models is the ability to forecast a non-divergent mortality for two or more sub-populations. One of the coherent models was recently developed by [1] known as the product-ratio model. This model is an extension version of the functional independent model from [2]. The product-ratio model has been applied in a developed country, Australia [1] and has been extended in a developing nation, Malaysia [3]. While [3] accounted for coherency of mortality rates between gender and ethnic group, the coherency between states in Malaysia has never been explored. This paper will forecast the mortality rates of Malaysian sub-populations according to states using the product ratio coherent model and its independent version-the functional independent model. The forecast accuracies of two different models are evaluated using the out-of-sample error measurements-the mean absolute forecast error (MAFE) for age-specific death rates and the mean forecast error (MFE) for the life expectancy at birth. We employ Malaysian mortality time series data from 1991 to 2014, segregated by age, gender and states.