For example, There is no doubt that global sea level is rising, and based on the global mean sea level (GMSL)data, we can calculated the trend of the GMSL. However, we all know that that must be some interannual/decadal variations of the GMSL, and even the alising errors of our data. We can get the linear trend of GMSL timeseires based on least-square method. However, how can we estimate the uncertainty range of this trend? 1, GMSL timeseires have autocorrelation; 2, the variations of GMSL timeseries are not the white noises, the standard deviation of GMSL anomalies is not 1.
I suggest that you employ an ARCH/ARMAX method where the ARCH component models the conditional variance of the error term, the ARMA component models the autoregressive nature of your data, and the X component models the effects of the exogenous variables.
Here is a link to a recent application of the method: Article CO 2 has significant implications for hourly ambient tempera...