In this case I am not sure what do you mean by "exists".
Can you give a definition, preferfably a hard one, that is, an algorithm into which I can feed the time series and it will tell me whether a particular feature (e.g. a hiatus) exists or not?
You're getting close to understanding the problem. What you're really asking about is an inference method, and the optimal inference method is Bayesian inference, which requires specification of what you would expect to see in the temperature record if the current warming rate were zero and also the specification of a prior probability. For the latter, an uninformative prior assigning equal weight to warming and cooling would probably be most suitable here. The former is a bit tricky, and that is precisely the problem with saying "the existence of the hiatus is obvious."
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
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