The Kmart change point analysis, while still crude, is pretty useful. Above is the GISS tropics, the best indication of applied energy from the sun. This plot shows one obvious anomaly, the tropics shifted in response of solar energy input. The 11 year linear regressions in this case are centered. With this orientation, climate "shifted" roughly in 1971. There is also an interesting anomaly around 1920, an "M" which is an indication of a saddle node perturbation.
Between the obvious peaks related to shifts and the more subtle saddle node "M" signatures, there is likely reasonable climate predictability "IF" natural variability and "unforced variations" are taken seriously by focusing on internal ocean oscillations instead of more chaotic atmospheric oscillations.