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

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  • Rodrigo Saul Gaitan
  • Keh‐Shin Lii

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.

Suggested Citation

  • Rodrigo Saul Gaitan & Keh‐Shin Lii, 2021. "On the Estimation of Periodicity or Almost Periodicity in Inhomogeneous Gamma Point‐Process Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(5-6), pages 711-736, September.
    • Handle: RePEc:bla:jtsera:v:42:y:2021:i:5-6:p:711-736
    DOI: 10.1111/jtsa.12585
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    References listed on IDEAS

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    1. Rodrigo Saul Gaitan & Keh-Shin Lii, 2021. "The first and second order moment structure of an inhomogeneous gamma point process," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(3), pages 582-593, February.
    2. Nan Shao & Keh‐Shin Lii, 2011. "Modelling non‐homogeneous Poisson processes with almost periodic intensity functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 99-122, January.
    3. P. A. W Lewis & G. S. Shedler, 1979. "Simulation of nonhomogeneous poisson processes by thinning," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 26(3), pages 403-413, September.
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