Generation of FARIMA(0,α,0) sequences by recursive filtering: Testing for self-similarity

This paper describes an approximate method for synthesizing sequences of statistically self-similar processes and analyses its performance to generate sample sequences with long-range dependence. The method is based upon approximating the infinite dimensional difference equation which describes the FARIMA(0,α,0) model by a finite dimensional difference equation. The parameters estimation for parameterizing the binomial coefficients is performed by deterministic signal modeling techniques (Prony, Shanks and Steiglitz MAcBride). In addition to allow considerable savings in memory requirements and great reduction in computation time, the performance analysis results show that the generated sequences are statistically self-similar in the sense that the estimated Hurst parameter is very close to that imposed in the sequences generator.