A first-order spatial integer-valued autoregressive \(\mathrm{SINAR}(1,1)\) model. (English) Zbl 1270.62128
Summary: The binomial thinning operator has a major role in modeling one-dimensional integer-valued autoregressive time series models. The purpose of this article is to extend the use of such operator to define a new stationary first-order spatial non-negative, integer-valued autoregressive \(\mathrm{SINAR}(1,1)\) model. We study some properties of this model like the mean, variance and autocorrelation function. the Yule-Walker estimator of the model parameters is also obtained. Some numerical results of the model are presented and, moreover, this model is applied to a real data set.
MSC:
| 62M30 | Inference from spatial processes |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62M09 | Non-Markovian processes: estimation |
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