  Many real time-series exhibit behavior adequate to long range dependent data.
Additionally very often these time-series have constant time periods and also
have characteristics similar to Gaussian processes although they are not
Gaussian. Therefore there is need to consider new classes of systems to model
these kind of empirical behavior. Motivated by this fact in this paper we
analyze two processes which exhibit long range dependence property and have
additional interesting characteristics which may be observed in real phenomena.
Both of them are constructed as the superposition of fractional Brownian motion
(FBM) and other process. In the first case the internal process, which plays
role of the time, is the gamma process while in the second case the internal
process is its inverse. We present in detail their main properties paying main
attention to the long range dependence property. Moreover, we show how to
simulate these processes and estimate their parameters. We propose to use a
novel method based on rescaled modified cumulative distribution function for
estimation of parameters of the second considered process. This method is very
useful in description of rounded data, like waiting times of subordinated
processes delayed by inverse subordinators. By using the Monte Carlo method we
show the effectiveness of proposed estimation procedures.
