Predicting Global Temperature Anomaly: A Definitive Investigation Using an Ensemble of Twelve Competing Forecasting Models

In this paper we analyze whether (anthropometric) CO$_2$ can forecast global temperature anomaly (GT) over an annual out-of-sample period of 1907-2012, which corresponds to an initial in-sample of 1880-1906. For our purpose, we use 12 parametric and nonparametric univariate (of GT only) and multivariate (including both GT and CO$_{2}$) models. Our results show that the Horizontal Multivariate Singular Spectral Analysis (HMSSA) techniques (both Recurrent (-R) and Vector (-V)) consistently outperform the other competing models. More importantly, from the performance of the HMSSA-V model we find conclusive evidence that CO$_2$ can forecast GT, and also predict its direction of change. Our results highlight the superiority of the nonparametric approach of SSA, which in turn, allows us to handle any statistical process: linear or nonlinear, stationary or non-stationary, Gaussian or non-Gaussian.