Forecasting paleoclimatic data with time series models

Abstract

Until recently, one obstacle to forecasting paleoclimatic data with time series models was gaps in the record. In 2020, highly resolved data sets became available. Time series models make it possible to determine how accurately climate can be predicted using techniques such as regressions and artificial intelligence. This paper runs forecasting tests for δ¹⁸O and δ¹³C using data spanning 34 Ma. The data exhibit several features: long-memory, irregular trending, and nonlinear variability. The probability distribution has heavy tails, and there are intermittent outliers. Because of the repeated changes in state, a simple train-validate-forecast method is inappropriate for these data sets. Instead, the testing methodology is iterative forecasting over moving windows: only recent observations are used to predict the future. There are several findings. First, at horizons of 2–4 kyr, all the methods perform well. Regressions and neural networks including the orbital parameters achieve the most accurate predictions for δ¹⁸O. In the tests for δ¹³C, the contest between the models is much closer. Second, as the horizon extends, accuracy deteriorates. At 10 kyr, the models track the central tendency of the data but miss the fluctuations. Third, forecast accuracy is found to vary substantially over time. There is a marked deterioration in accuracy starting around 2.58 Ma, coinciding with a period of steeper trending and greater amplitude in the cyclical fluctuations. The main limitation of time series models is that they do not incorporate the underlying physics. A more effective approach may be to combine statistical and physics-based models.