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Generalized Autoregressive Multivariate Models: From Binary to Poisson

Anna Bykhovskaya, Nour Meddahi

arXiv 15 Apr 2026 · Econometrics

arXiv:2604.14394 · PDF · DOI · OpenAlex · Extracted main text

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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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Fokianos, Konstantinos and Moysiadis, Theodoros (2017) Binary time series models driven by a latent process1.00053100%
2Moysiadis, Theodoros and Fokianos, Konstantinos (2014) On binary and categorical time series models with feedback1.00053100%
3Aknouche, Abdelhakim and Francq, Christian (2021) Count and duration time series with equal conditional stochastic and mean orders0.92843100%
4Lee, Sangyeol and Kim, Dongwon and Kim, Byungsoo (2023) Modeling and inference for multivariate time series of counts based on the INGARCH scheme0.92843100%
5Fokianos, Konstantinos and Rahbek, Anders and Tjøstheim, Dag (2009) Poisson autoregression0.81142100%
6Creal, Drew and Koopman, Siem Jan and Lucas, André (2013) Generalized autoregressive score models with applications0.73732100%
7Bollerslev, Tim (1986) Generalized autoregressive conditional heteroskedasticity0.64422100%
8Ferland, René and Latour, Alain and Oraichi, Driss (2006) Integer-valued GARCH process0.64422100%
9Rydberg, Tina Hviid and Shephard, Neil (2000) A modelling framework for the prices and times of trades made on the New York stock exchange0.51121100%
10Blasques, Francisco and Koopman, Siem Jan and Lucas, André (2014) Stationarity and ergodicity of univariate generalized autoregressive score processes0.40511100%

Showing the top 10 of 24 scored citations.