David Tweed wrote:

> the fact (that) pca seems virtually as good as other techniques is interesting.

Being able to detect signals using linear models is a seemingly signficant finding I took from the thesis.

Julian Sligo and Tim Palmer wrote in the paper Peter cited above, wrote:

> However, these empirical correction methods are essentially linear and yet we know that the real system is highly nonlinear. As Turner et al. [16] have demonstrated, there is inherently much more predictive skill if improvements in model formulation could be made that reduce these biases, rather than correcting them after the fact.

This suggests that an important way forward is to improve the performance of non-linear dynamic models. I'm not sure where that leaves non-linear statistical analysis of the observations.