A finite-state stationary process with long-range dependence and fractional multinomial distribution

TL;DR

This paper introduces a novel finite-state stationary process capable of exhibiting long-range dependence with state-specific Hurst indices and heavy-tailed inter-arrival times, enabling modeling of over-dispersed multinomial distributions.

Contribution

It presents a new discrete-time process with state-dependent long-range dependence and heavy tails, and defines a fractional multinomial distribution based on this model.

Findings

Process can model different long-range dependencies per state

Inter-arrival times follow heavy tail distributions with varying tails

Defines fractional multinomial distribution for over-dispersed data

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 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.