ASYMPTOTIC DISTRIBUTION OF MAXIMAL AUTOREGRESSIVE PROCESS WITH WEIGHT TENDING TO 1

NOBUO INAGAKI

Department of Mathematical Science, Osaka University, Toyonaka, Osaka 560, Japan

(Received March 26, 1993; revised June 8, 1994)

Abstract. The maximal operator plays the similar role as the summation operator in the sense of stability of operation. So, we could discuss ARMA processes in the maximal operation by the same way as in the summation operation. However, many papers already treated with moving order statistics. In this paper, we discuss asymptotic behaviors of maximal autoregressive (MAR) processes with the weight tending to 1.

Key words and phrases: Extreme value distribution, stability coefficients, maximal autoregressive process, maximum of weighted random variables.