I have analyzed several water temperature time series using a statistical method that I have developed and published. There is not stable cycle in the el nino temps nor is there any stable time structure in the Darwin data.
But there are stable cycles in the sun’s radiation due to a proven theory of the mechanism for a star’s high temperature. Also the daily sun spots have a stable cycle with some variation.
I once visited a young physicist at the Harwell climate laboratory in England. We discussed some of my work. I asked him how they calibrated their model with data. He told me that there are not enough data point of the Earth per year plus insufficiently long time series for them to calibrate the model. Then he said “I don’t really believe in our predictions but I have to make a living”. This from a scientist in one of the world’s best climate shops.