A hybrid recursive direct system for multi-step mortality rate forecasting

Forecasting mortality is challenging. In general, mortality rate forecasting exercises have been based on the supposition that predictors’ residuals are random noise. However, issues regarding model selection, misspecification, or the dynamic behavior of the temporal phenomenon lead to biased or underperformed single models. Residual series might present temporal patterns that can still be used to improve the forecasting system. This paper proposes a new recursive direct multi-step Hybrid System for Mortality Forecasting (HyS-MF) that combines the Autoregressive Integrated Moving Average (ARIMA) with Neural Basis Expansion for Time Series Forecasting (N-BEATS). HyS-MF employs (i) ARIMA to model and forecast the mortality rate time series with a recursive approach and (ii) N-BEATS with the direct multi-step approach to learn and forecast the residuals of the linear predictor. The final output is generated by summing ARIMA with the N-BEATS forecasts in each time horizon. HyS-MF achieved an average Mean Absolute Percentage Error (MAPE) less than 1.34% considering all prediction horizons, beating statistical techniques, machine learning, deep learning models, and hybrid systems considering 101 different time series from the French population mortality rate.