On the self-similarity of 1/fβ sequences synthesized by recursive filtering

This paper describes an approximate method for synthesizing sequences of statistically self-similar processes and analyses its performance to generate sample sequences with this statistical property. 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 using deterministic signal modeling techniques. The three techniques considered are: Prony, Steiglitz MacBride, and Shaw methods. 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 sequence generator.

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► Approximation of the FARIMA(0, α, 0) model by a finite dimensional difference equation.
► Computationally efficient Synthesis of sequences of FARIMA(0, α, 0) processes.
► The generated sequences are approximately statistically self-similar.