Robust non-parametric mortality and fertility modelling and forecasting: Gaussian process regression approaches

TL;DR

This paper tackles the challenge of forecasting mortality and fertility movements in developed countries by introducing a non-parametric Gaussian process regression framework that treats each age-specific time series as an independent Gaussian process. It uses a natural cubic spline mean function to capture recent trends and a spectral mixture covariance to model non-linearities and periodic patterns, enabling dense, per-age curve fitting and robust short-, mid-, and long-term forecasts. Empirical results on Japan’s mortality and fertility data, plus rolling-window evaluations across ten countries, show that the proposed GPR approach often achieves lower forecast errors than traditional demographic models (Lee-Carter, Lee-Miller, Booth-Maindonald-Smith, Hyndman-Ullah), highlighting improved precision and robustness. The work demonstrates significant practical value for policy planning and resource budgeting, and points to future extensions to multi-output GPR to exploit cross-age correlations for even stronger demographic forecasts.

Abstract

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.

Figures (12)

• Figure 4.2: Predicted male mortality rates of the selected age groups from age 0 to age 100 with 20-year age intervals using the proposed GPR model for the year 2007 to the year 2016 based on the observations from the year 1947 to the year 2006 in Japan. The solid lines are the observed values, and the dashed lines are the predictive mean and the 95% prediction intervals. The vertical line indicates the starting point of the predictions.
• Figure 4.3: Predicted male mortality curve from age 0 to age 100 with 95% prediction intervals using the proposed GPR model for the year 2016 based on the observations from the year 1947 to the year 2006 in Japan. The circles are the true log mortality rates, the solid line is the predictive mean, and the dashed lines are the 95% prediction intervals.
• Figure 4.5: Predicted fertility rates of the selected age groups from age 15 to age 45 with 5-year age intervals using the GPR model from the year 2007 to the year 2016 based on the observations from the year 1947 to the year 2006 in Japan. The solid lines are the observed values, and the dashed lines are the predictive mean and the 95% prediction intervals. The vertical line indicates the starting point of the predictions.
• Figure 4.6: Predicted fertility curve from age 15 to age 45 with 95% prediction intervals using the GPR model for the year 2016 based on the observations from the year 1947 to the year 2006 in Japan. The circles are the true log fertility rates, the solid line is the predictive mean, and the dashed lines are the 95% prediction intervals.
• Figure 4.7: Predicted male mortality curves from age 0 to age 100 for the year 2016 using the LC model (with RMSE = 0.2172), the LM model (with RMSE = 0.1660), the BMS model (with RMSE = 0.1109), the HU model (with RMSE = 0.2342) and the GPR model (with RMSE = 0.0895) based on the observations from the year 1947 to the year 2006 in Japan.