A simple El Nino prediction scheme using the signature of climate time series

We construct a El Nino prediction model based on the machine learning of the time series of climate indices. By transforming the multidimensional time series into path signature, we were able to properly evaluate the order and nonlinearity of climate events, which allowed us to achieve a good forecasting skill (mean square error = 0.506 for 6-month prediction). In addition, it is possible to provide information about which sequence of climate events tend to change the future Nino 3.4 SST. In our forecasting experiment, the changes in the North Pacific Index and various NINO indices were found to be important precursors.