Functional linear models for mortality forecasting

Over the last two decades, a number of approaches have been developed for modeling and forecasting mortality rates. However, using these models for two or more groups leads to inconsistent results, and various approaches have been proposed to resolve this problem. In this thesis, I present two new classes of functional linear models for analyzing, modeling and forecasting multiple time series corresponding to age-specific mortality rates of two or more groups within similar populations, which have related dynamics. Such groups might be males and females in the same population, different parts of a country (e.g. different provinces and states), races within a country (such as African American, White and Hispanic women in the United States), or different countries within a particular geographical region (for example, countries in the G7 group). The definition of “group” here depends on the forecaster’s judgement. It is desirable for the disaggregated forecasts to be coherent with the overall forecast. In particular, a common restriction is that the sub-group forecasts should not diverge in the long run, and that the relative mortality rates of the sub-groups should be approximately the same in the forecast period as in the historical period. This thesis is concerned with both theoretical and methodological developments of coherent mortality forecasting and the practical application of these new methods to various problems of real and current interest. I develop methods that are suitable for forecasting not only all-cause mortality data, but also cause-specific mortality, such as mortality rates of chronic diseases, in contrast to the traditional age-period-cohort models. The first contribution of this thesis is to obtain age-related predictions of black and white breast cancer mortality rates in the United States. To the best of my knowledge, this is the first such study. I have successfully applied functional time series models to the breast cancer mortality data, as an alternative to the widely used APC models. I have shown that these models not only provide a basis for modeling age-specific mortality rates, but can also be used to provide mortality forecasts and prediction intervals. A new method for the coherent forecasting of two or more functional time series of mortality rates is proposed in chapter 4. This method is based on modelling the products and ratios of mortality rates from each individual group, rather than modelling the mortality rates themselves. The proposed method simplifies the modelling procedure greatly, and provides a convenient and interpretable way of imposing coherence on the resulting forecasts. Relative to other recent proposals for coherent forecasting, the new approach is simpler to apply, is more flexible in allowing different types of dynamics, and produces more accurate forecasts. In this thesis, I relate some of the model extensions proposed by Hyndman & Ullah (2007), to the common principal components (CPC) and partial common principal components (PCPC) models introduced by Flury (1988). I combine the ideas of functional principal components and CPC analysis with time series, and call the resulting models common functional principal component (CFPC) models. I then use these models for the coherent forecasting of mortality rates. Although Hyndman & Ullah (2007) proposed these models, they did not discuss how they might be estimated or implemented. I therefore provide the methods for parameter estimation and forecasting using these models. I propose a sequential procedure to estimate the common and non-common/specific components, and use vector error correction models (VECM) to forecast the specific time series coefficients. I have applied the new methods to several types of disaggregated mortality rate data (disaggregated by sex, by region and by race). The newly developed functional linear models allow for non-divergence constraints to be imposed simply and naturally. Through the application of these new forecasting methods to the breast cancer mortalitydata of black and white women in the United States, I have found that the breast cancer mortality rates for both races are expected to decline, with the mortality rates of blacks remaining higher than those of whites for all age-groups. My analysis suggests that black women do not benefit equally from mammography and screening programs, and that a Forecasting disparity between the breast cancer mortality rates of the two races is expected to continue into the future.