Teleconnections are prominent features of internal variability which, along with climatic means, can also undergo forced changes. The assessment of such changes based on single realization observational data calculating moving window temporal correlation coefficients is burdened by biases. Previously, we attributed one source of such a bias, that is, nonergodicity, to the omission of low-frequency (LF) variability, but find here that it is negligible for typical processes due to their spectral characteristic, given that LF, say, interdecadal, variability is much weaker than the high frequency interannual variability. The unnecessary omission of detrending, as another source, is potentially much more deleterious, as we find that the bias depends quadratically on both the window size and the trends of the means. Given that forced changes in the variances should not introduce much bias, a nonlinear change of the teleconnection strength is implied as the main irreducible source of nonergodicity.