Extreme Value Theory for Moving Average Processes

Abstract

This paper studies extreme values in infinite moving average processes Xt = ∑λ cλ - t Zλ defined from an i.i.d. noise sequence {Zλ}. In particular this includes the ARMA-processes often used in time series analysis. A fairly complete extremal theory is developed for the cases when the d.f. of the Zλ's has a smooth tail which decreases approximately as exp{- zp} as z → ∞, for $0 < p