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A Note on the Innovation Distribution of a Gamma Distributed Autoregressive Process

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  • S. G. Walker

Abstract

A representation of the innovation random variable for a gamma distributed first‐order autoregressive process was found by Lawrance (1982) in the form of a compound Poisson distribution, connected with a shot‐noise process. In this note we simplify the representation of Lawrance by providing a direct representation in terms of density functions.

Suggested Citation

  • S. G. Walker, 2000. "A Note on the Innovation Distribution of a Gamma Distributed Autoregressive Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(3), pages 575-576, September.
    • Handle: RePEc:bla:scjsta:v:27:y:2000:i:3:p:575-576
    DOI: 10.1111/1467-9469.00208
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    Cited by:

    1. Paola Bortot & Carlo Gaetan, 2016. "Latent Process Modelling of Threshold Exceedances in Hourly Rainfall Series," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(3), pages 531-547, September.
    2. Luis Nieto-Barajas & Eduardo Gutiérrez-Peña, 2022. "General dependence structures for some models based on exponential families with quadratic variance functions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 699-716, September.
    3. Paola Bortot & Carlo Gaetan, 2014. "A Latent Process Model for Temporal Extremes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 606-621, September.

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