  We study simple approximations to fractional Gaussian noise and fractional
Brownian motion. The approximations are based on spectral properties of the
noise. They allow one to consider the noise as the result of fractional
integration/differentiation of a white Gaussian noise. We study correlation
properties of the approximation to fractional Gaussian noise and point to the
peculiarities of persistent and anti-persistent behaviors. We also investigate
self-similar properties of the approximation to fractional Brownian motion,
namely, ``tH laws`` for the structure function and the range. We conclude that
the models proposed serve as a convenient tool for the natural processes
modelling and testing and improvement of the methods aimed at analysis and
interpretation of experimental data.
