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Generalized Autoregressive Multivariate Models: From Binary to Poisson

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  • Anna Bykhovskaya
  • Nour Meddahi

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.

Suggested Citation

  • Anna Bykhovskaya & Nour Meddahi, 2026. "Generalized Autoregressive Multivariate Models: From Binary to Poisson," Papers 2604.14394, arXiv.org.
    • Handle: RePEc:arx:papers:2604.14394
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    File URL: http://arxiv.org/pdf/2604.14394
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