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arXiv · 2604.14394

Generalized Autoregressive Multivariate Models: From Binary to Poisson

Anna Bykhovskaya·Nour Meddahi
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Abstract

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.

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Anna Bykhovskaya, Nour Meddahi. 2026-04-15. Generalized Autoregressive Multivariate Models: From Binary to Poisson. https://arxiv.org/abs/2604.14394

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