  A rapid decline in mortality and fertility has become major issues in many
developed countries over the past few decades. A precise model for forecasting
demographic movements is important for decision making in social welfare
policies and resource budgeting among the government and many industry sectors.
This article introduces a novel non-parametric approach using Gaussian process
regression with a natural cubic spline mean function and a spectral mixture
covariance function for mortality and fertility modelling and forecasting.
Unlike most of the existing approaches in demographic modelling literature,
which rely on time parameters to decide the movements of the whole mortality or
fertility curve shifting from one year to another over time, we consider the
mortality and fertility curves from their components of all age-specific
mortality and fertility rates and assume each of them following a Gaussian
process over time to fit the whole curves in a discrete but intensive style.
The proposed Gaussian process regression approach shows significant
improvements in terms of preciseness and robustness compared to other
mainstream demographic modelling approaches in the short-, mid- and long-term
forecasting using the mortality and fertility data of several developed
countries in our numerical experiments.
