On non-stationarity of the Poisson gamma state space models
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866915681311653888 |
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| author | Irie, Kaoru Aktekin, Tevfik |
| author_facet | Irie, Kaoru Aktekin, Tevfik |
| contents | The Poisson-gamma state space (PGSS) models have been utilized in the analysis of non-negative integer-valued time series to sequentially obtain closed form filtering and predictive densities. In this study, we show the underlying mechanics and non-stationary properties of multi-step ahead predictive distributions for the PGSS family of models. By exploiting the non-stationary structure of the PGSS model, we establish that the predictive mean remains constant while the predictive variance diverges with the forecast horizon, a property also found in Gaussian random walk models. We show that, in the long run, the predictive distribution converges to a zero-degenerated distribution, such that both point and interval forecasts eventually converge towards zero. In doing so, we comment on the effect of hyper-parameters and the discount factor on the long-run behavior of the forecasts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15128 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On non-stationarity of the Poisson gamma state space models Irie, Kaoru Aktekin, Tevfik Methodology 62F15 Bayesian inference, 62M10 Time series The Poisson-gamma state space (PGSS) models have been utilized in the analysis of non-negative integer-valued time series to sequentially obtain closed form filtering and predictive densities. In this study, we show the underlying mechanics and non-stationary properties of multi-step ahead predictive distributions for the PGSS family of models. By exploiting the non-stationary structure of the PGSS model, we establish that the predictive mean remains constant while the predictive variance diverges with the forecast horizon, a property also found in Gaussian random walk models. We show that, in the long run, the predictive distribution converges to a zero-degenerated distribution, such that both point and interval forecasts eventually converge towards zero. In doing so, we comment on the effect of hyper-parameters and the discount factor on the long-run behavior of the forecasts. |
| title | On non-stationarity of the Poisson gamma state space models |
| topic | Methodology 62F15 Bayesian inference, 62M10 Time series |
| url | https://arxiv.org/abs/2512.15128 |