A limit theorem for the maximum term in a particular EARMA(1, 1) sequence
- 1 September 1980
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 17 (3) , 869-873
- https://doi.org/10.2307/3212983
Abstract
The EARMA(1, 1) process was described by Jacobs and Lewis (1977). Chernick (1978) showed that the limit for the maximum term is the same as for a sequence of independent, identically distributed exponential random variables when the parameter ρ is less than 1. When ρ = 1, a different limit theorem is obtained. The resulting limit distribution is not an extreme-value type. It is, however, of the general form given by Galambos (1978). The sequence is exchangeable.Keywords
This publication has 2 references indexed in Scilit:
- A mixed autoregressive-moving average exponential sequence and point process (EARMA 1,1)Advances in Applied Probability, 1977
- On extreme values in stationary sequencesProbability Theory and Related Fields, 1974