A Finite-State Stationary Process with Long-Range Dependence and Fractional Multinomial Distribution

Abstract

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 a different Hurst index for different states. Furthermore, 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 a fractional multinomial distribution from our model.