Giulia Carallo, Roberto Casarin, Christian P. Robert
arXiv 11 Feb 2020 · Statistics — Methodology · publishedInternational Journal of Forecasting (2023) · 10 citations (OpenAlex)
arXiv:2002.04470 · PDF · DOI · OpenAlex · Extracted main text
This paper introduces a new stochastic process with values in the set Z of integers with sign. The increments of process are Poisson differences and the dynamics has an autoregressive structure. We study the properties of the process and exploit the thinning representation to derive stationarity conditions and the stationary distribution of the process. We provide a Bayesian inference method and an efficient posterior approximation procedure based on Monte Carlo. Numerical illustrations on both simulated and real data show the effectiveness of the proposed inference.
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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 | Ferland, R., Latour, A., and Oraichi, D (2006) Integer-valued GARCH process | 0.965 | 10 | 4 | 90% |
| 2 | Zhu, F (2012) Modeling overdispersed or underdispersed count data with generalized Poisson integer-valued GARCH models | 0.894 | 7 | 3 | 71% |
| 3 | Cunha, E. T. d., Vasconcellos, K. L., and Bourguignon, M (2018) A skew integer-valued time-series process with generalized Poisson difference marginal distribution | 0.874 | 5 | 2 | 100% |
| 4 | Wei, C. H (2008) Thinning operations for modeling time series of counts? A survey | 0.843 | 4 | 3 | 75% |
| 5 | Consul, P. C (1986) On the differences of two generalized Poisson variates | 0.843 | 5 | 4 | 60% |
| 6 | Alzaid, A. and Al-Osh, M (1993) Generalized Poisson ARMA processes | 0.830 | 7 | 3 | 57% |
| 7 | Kim, H.-Y. and Park, Y (2008) A non-stationary integer-valued autoregressive model | 0.811 | 4 | 2 | 100% |
| 8 | Wei, C. H (2009) Modelling time series of counts with overdispersion | 0.644 | 4 | 1 | 100% |
| 9 | Agrafiotis, I., Nurse, J. R. C., Goldsmith, M., Creese, S., and Upto… (2018) A taxonomy of cyber-harms: Defining the impacts of cyber-attacks and understanding how they propagate | 0.644 | 2 | 2 | 100% |
| 10 | Andersson, J. and Karlis, D (2014) A parametric time series model with covariates for integers in Z | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 93 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | A Dynamic Stochastic Block Model for Multidimensional Networks | 0.405 | 1 | 1 |