Abstract
Let {X k } be a stationary moving average sequence of the form X k = Σj = −∞∞ β j *Zk − j where {Z k } is an iid sequence of random variables with regularly varying tails, and the operator * denotes multiplication if Z k is continuous and binomial thinning if Z k is a non-negative integer-valued. Let \(g{\left( k \right)}:\mathbb{N}_{{\text{0}}} \to \mathbb{N}_{{\text{0}}} \) be a strictly increasing sequence with a periodic pattern of the form g(k + I) = g(k) + M for some fixed integers I and M verifying 1 ≤ I ≤ M. Define Y k = Xg(k) as the generalised periodic sub-sampled moving average sequence. In this work we look at the extremal properties of {Y k }. In particular, we investigate the limiting distribution of the sample maxima and the corresponding extremal index. Motivation comes from the comparison of schemes for monitoring a variety of medical, finance, environmental, and social science data sets.
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AMS 2000 Subject Classification. 62–02, 60G70, 60G10
Contract/grant sponsors: POCTI/33477/Mat/2000 and POSI/CPS/42069/2001 FCT plurianual funding.
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Hall, A., Scotto, M.G. & Ferreira, H. On the Extremal Behaviour of Generalised Periodic Sub-Sampled Moving Average Models with Regularly Varying Tails. Extremes 7, 149–160 (2004). https://doi.org/10.1007/s10687-005-6197-9
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DOI: https://doi.org/10.1007/s10687-005-6197-9