Extending recent work on stress fluctuations in complex fluids and amorphous solids we describe in general terms the ensemble average v(∆t) and the standard deviation δv(∆t) of the variance v[x] of time series x of a stochastic process x(t) measured over a finite sampling time ∆t. Assuming a stationary, Gaussian and ergodic process, δv is given by a functional δvG[h] of the autocorrelation function h(t). δv(∆t) is shown to become large and similar to v(∆t) if ∆t corresponds to a fast relaxation process. Albeit δv = δvG[h] does not hold in general for non-ergodic systems, the deviations for common systems with many microstates are merely finite-size corrections. Various issues are illustrated for shear-stress fluctuations in simple coarse-grained model systems.