Anna Bykhovskaya, Nour Meddahi
arXiv 15 Apr 2026 · Econometrics
arXiv:2604.14394 · PDF · DOI · OpenAlex · Extracted main text
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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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Fokianos, Konstantinos and Moysiadis, Theodoros (2017) Binary time series models driven by a latent process | 1.000 | 5 | 3 | 100% |
| 2 | Moysiadis, Theodoros and Fokianos, Konstantinos (2014) On binary and categorical time series models with feedback | 1.000 | 5 | 3 | 100% |
| 3 | Aknouche, Abdelhakim and Francq, Christian (2021) Count and duration time series with equal conditional stochastic and mean orders | 0.928 | 4 | 3 | 100% |
| 4 | Lee, Sangyeol and Kim, Dongwon and Kim, Byungsoo (2023) Modeling and inference for multivariate time series of counts based on the INGARCH scheme | 0.928 | 4 | 3 | 100% |
| 5 | Fokianos, Konstantinos and Rahbek, Anders and Tjøstheim, Dag (2009) Poisson autoregression | 0.811 | 4 | 2 | 100% |
| 6 | Creal, Drew and Koopman, Siem Jan and Lucas, André (2013) Generalized autoregressive score models with applications | 0.737 | 3 | 2 | 100% |
| 7 | Bollerslev, Tim (1986) Generalized autoregressive conditional heteroskedasticity | 0.644 | 2 | 2 | 100% |
| 8 | Ferland, René and Latour, Alain and Oraichi, Driss (2006) Integer-valued GARCH process | 0.644 | 2 | 2 | 100% |
| 9 | Rydberg, Tina Hviid and Shephard, Neil (2000) A modelling framework for the prices and times of trades made on the New York stock exchange | 0.511 | 2 | 1 | 100% |
| 10 | Blasques, Francisco and Koopman, Siem Jan and Lucas, André (2014) Stationarity and ergodicity of univariate generalized autoregressive score processes | 0.405 | 1 | 1 | 100% |
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