Extremes of periodic moving averages of random variables with regularly varying tail probabilities
We define a family of local mixing conditions that enable the computation of the extremal index of periodic sequences from the joint distributions of kconsecutive variables of the sequence. By applying results, under local and global mixing conditions, to the ( 2m – 1)–dependent periodic sequence X(...
| Authors: | ; |
|---|---|
| Format: | Article |
| Publication date: | 2004 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2099/3752 |
| Online Access: | https://hdl.handle.net/2099/3752 |
| Access Level: | Open access |
| Keyword: | Stochastic processes Processos estocàstics Classificació AMS::60 Probability theory and stochastic processes::60G Stochastic processes |
| Summary: | We define a family of local mixing conditions that enable the computation of the extremal index of periodic sequences from the joint distributions of kconsecutive variables of the sequence. By applying results, under local and global mixing conditions, to the ( 2m – 1)–dependent periodic sequence X(m) n = Pm – 1 j = –m cj Zn – j, n ≥ 1, we compute the extremal index of the periodic moving average sequence Xn= P∞ j=–∞ cj Zn – j, n ≥ 1, of random variables with regularly varying tail probabilities. This paper generalizes the theory for extremes of stationary moving averages with regularly varying tail probabilities. |
|---|