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    Integer-valued autoregressive processes with prespecified marginal and innovation distributions: a novel perspective

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    Type
    Article
    Authors
    Guerrero, Matheus B. cc
    Barreto-Souza, Wagner cc
    Ombao, Hernando cc
    KAUST Department
    Biostatistics Group
    Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
    Statistics Program
    KAUST Grant Number
    NIH 1R01EB028753-01
    Date
    2021-09-26
    Embargo End Date
    2022-09-26
    Permanent link to this record
    http://hdl.handle.net/10754/672018
    
    Metadata
    Show full item record
    Abstract
    Integer-valued autoregressive (INAR) processes are generally defined by specifying the thinning operator and either the innovations or the marginal distributions. The major limitations of such processes include difficulties in deriving the marginal properties and justifying the choice of the thinning operator. To overcome these drawbacks, we propose a novel approach for building an INAR model that offers the flexibility to prespecify both marginal and innovation distributions. Thus, the thinning operator is no longer subjectively selected but is rather a direct consequence of the marginal and innovation distributions specified by the modeler. Novel INAR processes are introduced following this perspective; these processes include a model with geometric marginal and innovation distributions (Geo-INAR) and models with bounded innovations. We explore the Geo-INAR model, which is a natural alternative to the classical Poisson INAR model. The Geo-INAR process has interesting stochastic properties, such as MA(∞) representation, time reversibility, and closed forms for the hth-order transition probabilities, which enables a natural framework to perform coherent forecasting. To demonstrate the real-world application of the Geo-INAR model, we analyze a count time series of criminal records in sex offenses using the proposed methodology and compare it with existing INAR and integer-valued generalized autoregressive conditional heteroscedastic models.
    Citation
    Guerrero, M. B., Barreto-Souza, W., & Ombao, H. (2021). Integer-valued autoregressive processes with prespecified marginal and innovation distributions: a novel perspective. Stochastic Models, 1–21. doi:10.1080/15326349.2021.1977141
    Sponsors
    We would also like to acknowledge support from the KAUST Research Fund (Grant No.: NIH 1R01EB028753-01). Part of this study was performed by Matheus B. Guerrero (Master’s Thesis) at the Department of Statistics of the Universidade Federal de Minas Gerais. W. Barreto-Souza also thanks Conselho Nacional de Desenvolvimento Científico e Tecnológico for financial support (CNPq-Brazil; grant number: 305543/2018-0).
    Publisher
    Informa UK Limited
    Journal
    Stochastic Models
    DOI
    10.1080/15326349.2021.1977141
    Additional Links
    https://www.tandfonline.com/doi/full/10.1080/15326349.2021.1977141
    ae974a485f413a2113503eed53cd6c53
    10.1080/15326349.2021.1977141
    Scopus Count
    Collections
    Articles; Statistics Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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