Common functional principal component models for mortality forecasting

We explore models for forecasting groups of functional time series data that exploit common features in the data. Our models involve fitting common (or partially common) functional principal component models and forecasting the coefficients using univariate time series methods. We illustrate our approach by forecasting age-specific mortality rates for males and females in Australia. 4.1 Functional time series models We are interested in forecasting groups of functional time series data. For example, the annual age-specific mortality rates for a country can be considered a functional time series, {f1(x), f2(x), . . . , fT (x)}, observed over years 1, . . . , T , where x denotes age. When we observe mortality rates for subsets of the population (e.g., split by sex, or by race, or by geographical region), we have grouped functional time series. Methods for forecasting functional time series data have been developed by [9, 8, 3, 13, 6]. A related but different problem involves forecasting a segmented continuous time series [1]. While our methods have application to this second problem, we will not consider it in this paper. The most common approach to the problem of forecasting a functional time series is to use a principal components decomposition [12] and then to use univariate time series models to forecast each of the principal component scores. Rob J Hyndman Monash University, Australia, e-mail: [email protected] Farah Yasmeen University of Karachi, Pakistan, e-mail: [email protected]