  We propose a discrete-time, finite-state stationary process that can possess
long-range dependence. Among the interesting features of this process is that
each state can have different long-term dependency, i.e., the indicator
sequence can have different Hurst index for different states. Also,
inter-arrival time for each state follows heavy tail distribution, with
different states showing different tail behavior. A possible application of
this process is to model over-dispersed multinomial distribution. In
particular, we define fractional multinomial distribution from our model.
