Extremes of moving averages of random variables from the domain of attraction of the double exponential distribution

Richard Davis and Sidney Resnick

Stochastic Processes and their Applications, 1988, vol. 30, issue 1, 41-68

Abstract: Let {Zn} be an iid sequence of random variables with common distribution F which belongs to the domain of attraction of exp{-e-x}. If in addition, F[epsilon]Sr([gamma]) (i.e.,limx-->[infinity] P[Z1+Z2>]/P[Z1>x]=d[epsilon](0, [infinity]) and , then it is shown that a point process based on the moving average process {Xn:=[Sigma][infinity]j=-[infinity]cjZn-j} converges weakly. A host of complementary results concerning extremal properties of {Xn} can then be derived from this convergence result. These include the convergence of maxima to extremal processes, the limit point process of exceedances, the joint limit distribution of the largest and second largest and the joint limit distribution of the largest and smallest. Convergence of a sequence of point processes based on the max-moving average process {V[infinity]n=-[infinity]cjZn-j} is also considered.

Keywords: subexponential; distributions; double; exponential; distribution; extreme; values; point; processes; moving; average; Poisson; random; measure (search for similar items in EconPapers)
Date: 1988
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Citations: View citations in EconPapers (11)

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