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Integer†Valued Autoregressive Models With Survival Probability Driven By A Stochastic Recurrence Equation

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  • Paolo Gorgi

Abstract

This paper proposes a new class of integer†valued autoregressive models with a dynamic survival probability. The peculiarity of this class of models lies in the specification of the survival probability through a stochastic recurrence equation. The proposed models can effectively capture changing dependence over time and enhance both the in†sample and out†of†sample performance of integer†valued autoregressive models. This point is illustrated through an empirical application to a real†time series of crime reports. Additionally, this paper discusses the reliability of likelihood†based inference for the class of models. In particular, this study proves the consistency of the maximum likelihood estimator and a plug†in estimator for the conditional probability mass function in a misspecified model setting.

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  • Paolo Gorgi, 2018. "Integer†Valued Autoregressive Models With Survival Probability Driven By A Stochastic Recurrence Equation," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(2), pages 150-171, March.
    • Handle: RePEc:bla:jtsera:v:39:y:2018:i:2:p:150-171
    DOI: 10.1111/jtsa.12272
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    Cited by:

    1. Leisen, Fabrizio & Mena, Ramsés H. & Palma, Freddy & Rossini, Luca, 2019. "On a flexible construction of a negative binomial model," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 1-8.
    2. Mirko Armillotta & Paolo Gorgi, 2023. "Pseudo-variance quasi-maximum likelihood estimation of semi-parametric time series models," Tinbergen Institute Discussion Papers 23-054/III, Tinbergen Institute.
    3. Paolo Gorgi, 2020. "Beta–negative binomial auto‐regressions for modelling integer‐valued time series with extreme observations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(5), pages 1325-1347, December.
    4. Kai Yang & Han Li & Dehui Wang & Chenhui Zhang, 2021. "Random coefficients integer-valued threshold autoregressive processes driven by logistic regression," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(4), pages 533-557, December.
    5. Huaping Chen & Qi Li & Fukang Zhu, 2022. "A new class of integer-valued GARCH models for time series of bounded counts with extra-binomial variation," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(2), pages 243-270, June.
    6. Giovanni Angelini & Giuseppe Cavaliere & Enzo D'Innocenzo & Luca De Angelis, 2022. "Time-Varying Poisson Autoregression," Papers 2207.11003, arXiv.org.
    7. Francisco Blasques & Vladim'ir Hol'y & Petra Tomanov'a, 2018. "Zero-Inflated Autoregressive Conditional Duration Model for Discrete Trade Durations with Excessive Zeros," Papers 1812.07318, arXiv.org, revised May 2024.

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