Using Nonlinear Autoregressive Models with Exogenous Input to Analyze Temperature-Related Human Mortality

Recently, artificial neural network-based time series models known as nonlinear autoregressive models with exogenous input (NARX models) have been employed to examine various environmental phenomenon. This research presents an initial foray into the use of these NARX models in analyzing the relationship between daily temperature and human mortality across 41 different US cities, 1979-2010. In terms of model performance, across the US as a whole, median absolute percentage errors are 10.2% and the improvement in explained variability (over that of the simple 1-day autocorrelation) averages 18%. Generally, larger cities perform better in both metrics, and model performance is better in winter than in other seasons. Spike days in mortality (>80^th percentile) were also skillfully modeled, with a 54% hit rate on average across the US, and four cities performing at 70% or better. In terms of the temperature-mortality relationships, the association varies depending on season; the greatest amount of summer mortality occurs 0-2 days after a hot day (top 10 percentile), and the greatest winter mortality occurs about 2-4 days after a cold day (bottom 10 percentile), with this relationship being strongest in the more southern cities. While these relationships between temperature and mortality are in alignment with previous research, the modeling technique may prove advantageous as it assumes no a priori distribution, and it can be easily modified for multi-step ahead prediction.