Limit Theorem for the Maximum Term in an EARMA(1,1) Sequence when the Parameter rho Is One

摘要

The EARMA(1,1) process was defined by Jacobs and Lewis (Advances in Applied Probability, 1977). Chernick (Ph.D. dissertation, Stanford University, 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 rho is less than one. When rho equals one, 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 (The Asymptotic Theory of Extreme Order Statistics, Wiley, 1978). The sequence is exchangeable. (ERA citation 04:055900)