Self-similarity in max/average aggregated processes

Second-order self-similar processes are fully statically characterized by their activity factor and Hurst parameter, which are usually extracted from the computation of the autocovariance function of the process at different aggregation levels. Unfortunately, such an extraction procedure is difficult to be performed on experimental data or tested in analytical investigation. We here first aim at solving this problem by proposing a criterion to verify the self-similarity directly from the original process. Such a criterion is then applied to evaluate the self-similar features of the process obtained by averaging or maximizing the output of several independent sources. For both such cases we show that the resulting process is also self-similar with a higher Hurst parameter with respect to the original ones.