Robust Estimation and Forecasting of Climate Change Using Score-Driven Ice-Age Models

We use data on the following climate variables for the period of the last 798 thousand years: global ice volume ( Ice t ), atmospheric carbon dioxide level ( CO 2 , t ), and Antarctic land surface temperature ( Temp t ). Those variables are cyclical and are driven by the following strongly exogenous orbital variables: eccentricity of the Earth’s orbit, obliquity, and precession of the equinox. We introduce score-driven ice-age models which use robust filters of the conditional mean and variance, generalizing the updating mechanism and solving the misspecification of a recent climate–econometric model (benchmark ice-age model). The score-driven models control for omitted exogenous variables and extreme events, using more general dynamic structures and heteroskedasticity. We find that the score-driven models improve the performance of the benchmark ice-age model. We provide out-of-sample forecasts of the climate variables for the last 100 thousand years. We show that during the last 10–15 thousand years of the forecasting period, for which humanity influenced the Earth’s climate, (i) the forecasts of Ice t are above the observed Ice t , (ii) the forecasts of CO 2 , t level are below the observed CO 2 , t , and (iii) the forecasts of Temp t are below the observed Temp t . The forecasts for the benchmark ice-age model are reinforced by the score-driven models.