- University of Wollongong, 8 September 2010.
- Statistical Society of Australia, Victorian Branch, 28 September 2010.
- Updated version. September 2012.
Functional time series are curves that are observed sequentially in time. In demography, such data arise as the curves formed by annual death rates as a function of age or annual fertility rates as a function of age. I will discuss methods for describing, modelling and forecasting such functional time series data. Challenges include:
- developing useful graphical tools (I will illustrate a functional version of the boxplot);
- dealing with outliers (e.g., death rates have outliers in years of wars or epidemics);
- cohort effects (how can we identify and allow for these in the forecasts);
- synergy between groups (e.g, we expect male and female mortality rates to evolve in a similar way in the future);
- deriving prediction intervals for forecasts;
- how to combine the mortality and fertility forecasts to obtain forecasts of the total population.
I will illustrate the ideas using data from Australia and France.