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Flexible and Robust Mixed Poisson INGARCH Models

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  • Rodrigo B. Silva
  • Wagner Barreto‐Souza

Abstract

In this article, we propose a general class of INteger‐valued Generalized AutoRegressive Conditional Heteroskedastic (INGARCH) models based on a flexible family of mixed Poisson (MP) distributions. Our proposed class of count time series models contains the negative binomial (NB) INGARCH process as particular case and open the possibility to introduce new models such as the Poisson‐inverse Gaussian (PIG) and Poisson generalized hyperbolic secant processes. In particular, the PIG INGARCH model is an interesting and robust alternative to the NB model. We explore first‐order and second‐order stationary properties of our MPINGARCH models and provide expressions for the autocorrelation function and mean and variance marginals. Conditions to ensure strict stationarity and ergodicity properties for our class of INGARCH models are established. We propose an Expectation‐Maximization algorithm to estimate the parameters and obtain the associated information matrix. Further, we discuss two additional estimation methods. Monte Carlo simulation studies are considered to evaluate the finite‐sample performance of the proposed estimators. We illustrate the flexibility and robustness of the MPINGARCH models through two real‐data applications about number of cases of Escherichia coli and Campylobacter infections. This article contains a Supporting Information.

Suggested Citation

  • Rodrigo B. Silva & Wagner Barreto‐Souza, 2019. "Flexible and Robust Mixed Poisson INGARCH Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 40(5), pages 788-814, September.
    • Handle: RePEc:bla:jtsera:v:40:y:2019:i:5:p:788-814
    DOI: 10.1111/jtsa.12459
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    Cited by:

    1. Randal Douc & François Roueff & Tepmony Sim, 2021. "Necessary and sufficient conditions for the identifiability of observation‐driven models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(2), pages 140-160, March.
    2. Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos, 2020. "On an integer-valued stochastic intensity model for time series of counts," MPRA Paper 105406, University Library of Munich, Germany.
    3. Yuhyeong Jang & Raanju R. Sundararajan & Wagner Barreto-Souza & Elizabeth Wheaton-Paramo, 2024. "Determining economic factors for sex trafficking in the United States using count time series regression," Empirical Economics, Springer, vol. 67(1), pages 337-354, July.
    4. Wagner Barreto‐Souza & Hernando Ombao, 2022. "The negative binomial process: A tractable model with composite likelihood‐based inference," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 568-592, June.
    5. Wagner Barreto-Souza & Sokol Ndreca & Rodrigo B. Silva & Roger W. C. Silva, 2023. "Non-linear INAR(1) processes under an alternative geometric thinning operator," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 695-725, June.
    6. Luiza S. C. Piancastelli & Wagner Barreto‐Souza & Hernando Ombao, 2023. "Flexible bivariate INGARCH process with a broad range of contemporaneous correlation," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(2), pages 206-222, March.
    7. Aknouche, Abdelhakim & Scotto, Manuel, 2022. "A multiplicative thinning-based integer-valued GARCH model," MPRA Paper 112475, University Library of Munich, Germany.

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