Generalized Bernoulli process with long-range dependence and fractional binomial distribution

Lee Jeonghwa ()
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Lee Jeonghwa: Department of Statistics, Truman State University, USA

Dependence Modeling, 2021, vol. 9, issue 1, 1-12

Abstract: Bernoulli process is a finite or infinite sequence of independent binary variables, Xi, i = 1, 2, · · ·, whose outcome is either 1 or 0 with probability P(Xi = 1) = p, P(Xi = 0) = 1 – p, for a fixed constant p ∈ (0, 1). We will relax the independence condition of Bernoulli variables, and develop a generalized Bernoulli process that is stationary and has auto-covariance function that obeys power law with exponent 2H – 2, H ∈ (0, 1). Generalized Bernoulli process encompasses various forms of binary sequence from an independent binary sequence to a binary sequence that has long-range dependence. Fractional binomial random variable is defined as the sum of n consecutive variables in a generalized Bernoulli process, of particular interest is when its variance is proportional to n2H, if H ∈ (1/2, 1).

Keywords: Bernoulli process; Long-range dependence; Hurst exponent; over-dispersed binomial model (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:9:y:2021:i:1:p:1-12:n:1

DOI: 10.1515/demo-2021-0100

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