Evaluating direct and indirect evidence of climatic change by Hölder regularity and order pattern in time series

The several competing reconstructions of Northern Hemisphere temperature variability exists with partly conflicting evidence. Here we considered a specific problem of choosing “the best” reconstruction, in a frame of assumptions, that they are produced by smooth dynamical system as well as instrumental time series. Using some sophisticated measures of similarity, we could not match to all existing hemispheric paleoclimate reconstructions with hypothesis about any deterministic system which can produced its as typical projection of their trajectories. The results cast doubt on the conventional techniques frequently used to reconstruct past climate variability.