A batch means procedure for mean value estimation of processes exhibiting long range dependence

Mean value estimation of processes exhibiting long range dependence (LRD) requires a different approach than the techniques applied to those exhibiting short range dependence (SRD), except for the independent replication method. We describe a nonoverlapping batch means method able to deal with LRD processes, the LRD Batch Means method. This method exploits the behavior of asymptotically second-order self-similar processes: their aggregated processes become well approximated by fractional Gaussian noise (FGN) processes for large aggregation levels. Once tested positively for this similarity, the method produces a correlation-adjusted confidence interval from an empirical approximation of the distribution of the standardized average for the particular case of FGN processes. Afterwards, we measure its performance over both LRD and SRD processes.