Bellwether effect refers to the existence of exemplary projects (called the Bellwether) within a historical dataset to be used for improved prediction performance. Recent studies have shown an implicit assumption of using recently completed projects (referred to as moving window) for improved prediction accuracy. In this paper, we investigate the Bellwether effect on software effort estimation accuracy using moving windows. The existence of the Bellwether was empirically proven based on six postulations. We apply statistical stratification and Markov chain methodology to select the Bellwether moving window. The resulting Bellwether moving window is used to predict the software effort of a new project. Empirical results show that Bellwether effect exist in chronological datasets with a set of exemplary and recently completed projects representing the Bellwether moving window. Result from this study has shown that the use of Bellwether moving window with the Gaussian weighting function significantly improve the prediction accuracy.