This is a short course given at Humboldt University, Berlin, 24-25 June 2014.

**Venue:** LvB Library, Room 401, Spandauerstr. 1, 10178 Berlin

**Time:**
24 June 2014, 09:30 - 12:30 and 14:00 - 17:00
25 June 2014, 09:30 - 11:30

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]