Score-driven threshold ice-age models: benchmark models for long-run climate forecasts

Climate variables are known to be subject to abrupt changes when some threshold levels are surpassed. We use data for the last 798,000 years on global ice volume (Ice), atmospheric carbon dioxide level (CO2), and Antarctic land surface temperature (Temp) to model and measure those longrun nonlinear climate effects. The climate variables have very long and asymmetric cycles, created by periods of upward trends, followed by periods of downward trends driven by exogenous orbital variables. The exogenous orbital variables considered by the Milankovitch cycles are eccentricity of Earth's orbit, obliquity, and precession of the equinox. We show that our new score-driven threshold ice-age models improve the statistical inference and forecasting performance of competing ice-age models from the literature. The drawback of using our 1,000-year frequency observations, is that we cannot measure the nonlinear climate effects of humanity created during the last 250 years, which are known to have generated abrupt structural changes in the Earth's climate, due to unprecedented high levels of CO2 and Temp, and low levels of Ice volume. On the other hand, the advantage of using low-frequency data is that they allow us to obtain long-run forecasts on what would have occurred if humanity had not burned fossil fuels since the start of the Industrial Revolution. These long-run forecasts can serve as benchmarks for the long-run evaluation of the impact of humanity on climate variables. Without the impact of humanity on climate, we predict the existence of turning points in the evolution of the three climate variables for the next 5,000 years: an upward trend in global ice volume, and downward trends in atmospheric CO2 level and Antarctic land surface temperature.