From a pure time series perspective, you can apply econometrics-type tests for non-stationarity, such as a [unit root test]( But often people want to get at attribution, not just detection: is the change due to humans? For that, you need to compare to radiative forcing data. People tend to do multiple regression of temperature on forcings and various climatic indicators such as ENSO index, although there are also econometrics approaches like [Granger causality]( Personally, I don't really trust the econometrics approaches; regression is better, but I think you're better off building a simple climate model, like an energy balance model, and doing parameter estimation with that. It still will be more physically realistic than a regression.