Theory and inference for multivariate autoregressive binary models with an application to absence-presence data in ecology
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arXiv
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| Natura: | Preprint |
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2024
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| _version_ | 1866916323159703552 |
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| author | Franchi, Guillaume Truquet, Lionel |
| author_facet | Franchi, Guillaume Truquet, Lionel |
| contents | We introduce a general class of autoregressive models for studying the dynamic of multivariate binary time series with stationary exogenous covariates. Using a high-level set of assumptions, we show that existence of a stationary path for such models is almost automatic and does not require parameter restrictions when the noise term is not compactly supported. We then study in details statistical inference in a dynamic version of a multivariate probit type model, as a particular case of our general construction. To avoid a complex likelihood optimization, we combine pseudo-likelihood and pairwise likelihood methods for which asymptotic results are obtained for a single path analysis and also for panel data, using ergodic theorems for multi-indexed partial sums. The latter scenario is particularly important for analyzing absence-presence of species in Ecology, a field where data are often collected from surveys at various locations. Our results also give a theoretical background for such models which are often used by the practitioners but without a probabilistic framework. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_10260 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Theory and inference for multivariate autoregressive binary models with an application to absence-presence data in ecology Franchi, Guillaume Truquet, Lionel Statistics Theory We introduce a general class of autoregressive models for studying the dynamic of multivariate binary time series with stationary exogenous covariates. Using a high-level set of assumptions, we show that existence of a stationary path for such models is almost automatic and does not require parameter restrictions when the noise term is not compactly supported. We then study in details statistical inference in a dynamic version of a multivariate probit type model, as a particular case of our general construction. To avoid a complex likelihood optimization, we combine pseudo-likelihood and pairwise likelihood methods for which asymptotic results are obtained for a single path analysis and also for panel data, using ergodic theorems for multi-indexed partial sums. The latter scenario is particularly important for analyzing absence-presence of species in Ecology, a field where data are often collected from surveys at various locations. Our results also give a theoretical background for such models which are often used by the practitioners but without a probabilistic framework. |
| title | Theory and inference for multivariate autoregressive binary models with an application to absence-presence data in ecology |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2407.10260 |