Extremal Behavior of the Generalized Integer-Valued Random Coefficient Autoregressive Process
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Springer-Verlag Berlin Heidelberg
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.
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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.