Context: In addressing how best to estimate how much effort is required to develop software, a recent study found that using exemplary and recently completed projects [forming Bellwether moving windows (BMW)] in software effort prediction (SEP) models leads to relatively improved accuracy. More studies need to be conducted to determine whether the BMW yields improved accuracy in general, since different sizing and aging parameters of the BMW are known to affect accuracy. Objective: To investigate the existence of exemplary projects (Bellwethers) with defined window size and age parameters, and whether their use in SEP improves prediction accuracy. Method: We empirically investigate the moving window assumption based on the theory that the prediction outcome of a future event depends on the outcomes of prior events. Sampling of Bellwethers was undertaken using three introduced Bellwether methods (SSPM, SysSam, and RandSam). The ergodic Markov chain was used to determine the stationarity of the Bellwethers. Results: Empirical results show that 1) Bellwethers exist in SEP and 2) the BMW has an approximate size of 50 to 80 exemplary projects that should not be more than 2 years old relative to the new projects to be estimated. Conclusion: The study's results add further weight to the recommended use of Bellwethers for improved prediction accuracy in SEP.