On the Estimation of Periodicity or Almost Periodicity in Inhomogeneous Gamma Point‐Process Data

Rodrigo Saul Gaitan and Keh‐Shin Lii

Journal of Time Series Analysis, 2021, vol. 42, issue 5-6, 711-736

Abstract: The non‐homogeneous Poisson process (NHPP) and the renewal process (RP) are two stochastic point process models that are commonly used to describe the pattern of repeated occurrence data. An inhomogeneous Gamma process (IGP) is a point process model that generalizes both the NHPP and a particular RP, commonly referred to as a Gamma renewal process, which has interarrival times that are i.i.d. gamma random variables with unit scale parameter and shape parameter κ>0. This article focuses on a particular class of the IGP which has a periodic or almost periodic baseline intensity function and a shape parameter κ∈ℕ. This model deals with point events that show a pattern of periodicity or almost periodicity. Consistent estimators of unknown parameters are constructed mainly by the Bartlett periodogram. Simulation results that support theoretical findings are provided.

Date: 2021
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