As if to demonstrate that some climatic time series contain a lot less than you’d expect, here is the Armagh Maximum Temperature record from January 1844 to December 2004 (160 years)
Looks a lot like noise, doesn’t it?
As an example of what the record looks like on the scale of a few years:
Over to Fourier…
That peak is the annual cycle. There is no other periodic signal in the Armagh T-max record.
NB There were a very few missing values (days) which were pseudorandomly distributed. I infilled them with the mean of the entire series. They made no difference to the results of the analysis.