Statistical analysis of successive random additions for generating fractional Brownian motion

Successive random addition (SRA) is a popular and efficient algorithm for generating fractional Brownian motion (FBM). The difference of adjacent samples of FBM is called fractional Gaussian noise (FGN) and has a known self-similarity parameter H and power spectral density (PSD). For a FGN series generated from the differences of a SRA series, the intersample correlations for the first two lags are known to vary from the desired correlation. In this paper we show analytically and experimentally that the error in the correlations arises because the FGN generated from the differences of an SRA time-series is nonstationary.