On the long-range dependence of fractional Poisson and negative binomial processes

2016/12/01 by A. Maheshwari, Aditya Maheshwari, P. Vellaisamy · 5 citations
Economics, Econometrics and Finance · Mathematics · Computer Science · #Financial Risk and Volatility Modeling #Statistical Distribution Estimation and Applications #Bayesian Methods and Mixture Models

paper · doi:10.1017/jpr.2016.59

Abstract

Abstract We discuss the short-range dependence (SRD) property of the increments of the fractional Poisson process, called the fractional Poissonian noise. We also establish that the fractional negative binomial process (FNBP) has the long-range dependence (LRD) property, while the increments of the FNBP have the SRD property. Our definitions of the SRD/LRD properties are similar to those for a stationary process and different from those recently used in Biard and Saussereau (2014).

Citations

• Fractional Poisson Process: Long-Range Dependence and Applications in Ruin Theory

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