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Geometric infinitely divisible autoregressive models

Author

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  • Monika S. Dhull

    (Indian Institute of Technology Ropar)

  • Arun Kumar

    (Indian Institute of Technology Ropar)

Abstract

In this article, we discuss some geometric infinitely divisible (gid) random variables using the Laplace exponents which are Bernstein functions and study their properties. The distributional properties and limiting behavior of the probability densities of these gid random variables at $$0^{+}$$ 0 + are studied. The autoregressive (AR) models with gid marginals are introduced. Further, the first order AR process is generalized to kth order AR process. We also provide the parameter estimation method based on conditional least square and method of moments for the introduced AR(1) process. We also apply the introduced AR(1) model with geometric inverse Gaussian marginals on the household energy usage data which provide a good fit as compared to normal AR(1) data.

Suggested Citation

  • Monika S. Dhull & Arun Kumar, 2024. "Geometric infinitely divisible autoregressive models," Statistical Papers, Springer, vol. 65(7), pages 4515-4536, September.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:7:d:10.1007_s00362-024-01564-y
    DOI: 10.1007/s00362-024-01564-y
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    References listed on IDEAS

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    1. Kumar, A. & Vellaisamy, P., 2015. "Inverse tempered stable subordinators," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 134-141.
    2. B. Abraham & N. Balakrishna, 1999. "Inverse Gaussian Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(6), pages 605-618, November.
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