Change-point detection in functional time series: Applications to age-specific mortality and fertility

We consider determining change points in a time series of age-specific mortality and fertility curves observed over time. We propose two detection methods for identifying these change points. The first method uses a functional cumulative sum statistic to pinpoint the change point. The second method computes a univariate time series of integrated squared forecast errors after fitting a functional time-series model before applying a change-point detection method to the errors to determine the change point. Using Australian age-specific fertility and mortality data, we apply these methods to locate the change points and identify the optimal training period to achieve improved forecast accuracy.