Integer-valued autoregressive processes with prespecified marginal and innovation distributions: a novel perspective
KAUST DepartmentStatistics Program, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia
Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
KAUST Grant NumberNIH 1R01EB028753-01
Embargo End Date2022-09-26
Permanent link to this recordhttp://hdl.handle.net/10754/672018
MetadataShow full item record
AbstractInteger-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.
CitationGuerrero, 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
SponsorsWe 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).
PublisherInforma UK Limited