Hurst’s rescaled range statistical analysis for pseudorandom number generators used in physical simulations

The rescaled range statistical analysis $\mathrm{}(R/S)\mathrm{}$ is proposed as a method to detect correlations in pseudorandom number generators used in Monte Carlo simulations. In an extensive test it is demonstrated that the $R/S$ analysis provides a very sensitive method to reveal hidden long-run and short-run correlations. Several widely used and also some recently proposed pseudorandom number generators are subjected to this test. In many generators correlations are detected and quantified.