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Please use this identifier to cite or link to this item:
http://hdl.handle.net/10174/9646
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| Title: | Extremal Behavior of the Generalized Integer-Valued Random Coefficient Autoregressive Process |
| Authors: | Canto e Castro, Luísa
Gomes, Dulce
Temido, Maria da Graça |
| Editors: | Caeiro, Frederico |
| Keywords: | Extremal Behavior
Integer-valued Time Series
Autoregressive Process
Max-semistable Class
Anderson's Class |
| Issue Date: | Sep-2013 |
| Publisher: | Springer-Verlag Berlin Heidelberg |
| Citation: | Canto e Castro, L., Gomes, D. e Temido, M. G. (2013). Extremal Behavior of the Generalized Integer-Valued Random Coefficient Autoregressive Process. In Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications. Studies in Theoretical and Applied Statistics 2013, pp 93-101 (Lita da Silva, J.; Caeiro, F.; Natário, I.; Braumann, C.A. (Eds.)). ISBN: 9783642349034. |
| Abstract: | A stationary generalized random coefficient integer auto-regressive model of order 1 (Generalized RCINAR(1)), based on a thinning random operation, is presented. It is proved that the process satisfies a long range condition as well as a local dependence condition, which are appropriate extensions of the well known D(u_n) and D'(u_n) conditions of Leadbetter. Assuming that the marginal discrete distribution function belongs to Anderson's class, and then it does not belong to the domain of attraction of any max-stable distribution, the limit in distribution of the maximum of k_n random variables, being {k_n} a geometric growing sequence, is obtained. This limit is a discrete max-semistable distribution function usually called discretized Gumbel. |
| URI: | http://hdl.handle.net/10174/9646 |
| ISBN: | 9783642349034 |
| Type: | bookPart |
| Appears in Collections: | CIMA - Publicações - Capítulos de Livros
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