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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.
ISBN: 9783642349034
Type: bookPart
Appears in Collections:CIMA - Publicações - Capítulos de Livros

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