Generalized Autoregressive Multivariate Models: From Binary to Poisson
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914477180452864 |
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| author | Bykhovskaya, Anna Meddahi, Nour |
| author_facet | Bykhovskaya, Anna Meddahi, Nour |
| contents | This paper presents a framework for binary autoregressive time series in which each observation is a Bernoulli variable whose success probability evolves with past outcomes and probabilities, in the spirit of GARCH-type dynamics, accommodating nonlinearities, network interactions, and cross-sectional dependence in the multivariate case. Existence and uniqueness of a stationary solution is established via a coupling argument tailored to the discontinuities inherent in binary data. A key theoretical result, further supported by our empirical illustration on S&P 100 data, shows that, under a rare-events scaling, aggregates of such binary processes converge to a Poisson autoregression, providing a micro-foundation for this widely used count model. Maximum likelihood estimation is proposed and illustrated empirically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14394 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generalized Autoregressive Multivariate Models: From Binary to Poisson Bykhovskaya, Anna Meddahi, Nour Econometrics Statistics Theory This paper presents a framework for binary autoregressive time series in which each observation is a Bernoulli variable whose success probability evolves with past outcomes and probabilities, in the spirit of GARCH-type dynamics, accommodating nonlinearities, network interactions, and cross-sectional dependence in the multivariate case. Existence and uniqueness of a stationary solution is established via a coupling argument tailored to the discontinuities inherent in binary data. A key theoretical result, further supported by our empirical illustration on S&P 100 data, shows that, under a rare-events scaling, aggregates of such binary processes converge to a Poisson autoregression, providing a micro-foundation for this widely used count model. Maximum likelihood estimation is proposed and illustrated empirically. |
| title | Generalized Autoregressive Multivariate Models: From Binary to Poisson |
| topic | Econometrics Statistics Theory |
| url | https://arxiv.org/abs/2604.14394 |