Demographers often need to obtain individual forecasts of sub-groups within a population and it is desirable for the disaggregated forecasts to be coherent with the overall forecast. “Coherent” forecasts are non-divergent forecasts of subgroups within a population. In this paper, we intend to obtain coherent forecasts of breast cancer mortality data of black and white women in the United States. This is an application of coherent functional models of Hyndman et al. (2013) on the disaggregation of mortality forecasts by race. On the basis of previous studies, we found that black Americans have higher mortality rates and shorter survival times from breast cancer than white Americans. Here, we assume that the future breast cancer mortality rates of black women will remain higher than those of white women, for all age groups. We first describe the concept of coherence in the context of cause-specific mortality and discuss some problems with using independent functional time series models for the two races. Then, we apply the coherent functional model to the breast cancer mortality data. An empirical comparison of the independent and coherent models based on the breast cancer mortality data has been made. The purpose here is to see the performance of coherent forecasting models in the presence of disparity among the mortality rates of these two groups of American women, namely whites and blacks and to find whether the coherency is achieved in breast cancer mortality forecasting by this application.
Keywords:Forecasting, functional data analysis, coherent forecasts, breast cancer mortality, racial and ethnic disparities