On Long-Range Dependence of Markov Chains

Abstract

We look at the phenomena of long-range dependence (LRD) in stationary processes with finite variance. We present its characterizations based on autocorrelation functions, spectral density function and Allen variance. We focus this discussion on processes that are defined on discrete-time stationary Markov processes on countable state space and with a stationary one-step transition probabilities. The Markov chain is assumed to be irreducible and positive recurrent, and to simplify some aspects of the discussion without substantial loss of generality, we assume that the chain is aperiodic.