2015-7-12 Hyndman Functional time series with applications in demography

Hyndman

Abstract:

Functional time series are curves that are observed sequentially in time, one curve being observed in each time period. In demography, examples include curves formed by annual death rates as a function of age, or annual fertility rates as a function of age. In finance, functional time series can occur in the form of bond yield curves, for example, with each curve being the yield of a bond as a function of the maturity of a bond.

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, and we expect different types of yield curves to behave similarly over time);

deriving prediction intervals for forecasts;

how to combine mortality and fertility forecasts to obtain forecasts of the total population;

how to use these ideas to simulate the age-structure of future populations and use the results to analyse proposed government policies.

Lectures:

Tools for functional time series analysis [Slides]

Automatic time series forecasting [Slides]

Forecasting functional time series [Slides]

Connections, extensions and applications [Slides]

Forecasting functional time series via PLS [Slides]

Coherent functional forecasting [Slides]

Common functional principal components [Slides]

Stochastic population forecasting [Slides]