Bootstrap prediction intervals for the age distribution of life-table death counts

We introduce a nonparametric bootstrap procedure based on a dynamic factor model to construct pointwise prediction intervals for period life-table death counts. The age distribution of death counts is an example of constrained data, which are nonnegative and have a constrained integral. A centered log-ratio transformation is used to remove the constraints. With a time series of unconstrained data, we introduce our bootstrap method to construct prediction intervals, thereby quantifying forecast uncertainty. The bootstrap method utilizes a dynamic factor model to capture both nonstationary and stationary patterns through a two-stage functional principal component analysis. To capture parameter uncertainty, the estimated principal component scores and model residuals are sampled with replacement. Using the age- and sex-specific life-table deaths for Australia and the United Kingdom, we study the empirical coverage probabilities and compare them with the nominal ones. The bootstrap method has superior interval forecast accuracy, especially for the one-step-ahead forecast horizon.