The design and evaluation of the Simple Self-Similar Sequences Generator

This paper describes a new algorithm for the generation of pseudo random numbers with approximate self-similar structure. The Simple Self-Similar Sequences Generator (4SG) elaborates on an intuitive approach to obtain a fast and accurate procedure, capable of reproducing series of points exhibiting the property of persistence and anti-persistence  . 4SG has a computational complexity of O(n)O(n) and memory requirements of the order of log2(N)log2(N), where NN is the number of points to be generated. The accuracy of the algorithm is evaluated by means of computer-based simulations, recurring to several Hurst parameter estimators, namely Variance Time (VT) and the Wavelets-based estimator. The Hosking and the Wavelets-based methods for the generation of self-similar series were submitted to the same tests the 4SG was analysed with, providing for a basis for comparison of several performance aspects of the algorithm. Results show that the proposal embodies a good candidate not only for on-demand emulation of arbitrarily long self-similar sequences, but also for fast and efficient online simulations.