Limit Theory for Moving Averages of Random Variables with Regularly Varying Tail Probabilities

Abstract

Let $\{Z_k, -\infty < k < \infty\}$ be iid where the Z k 's have regularly varying tail probabilities. Under mild conditions on a real sequence {c j, j ≥ 0} the stationary process {X n : = ∑ ∞ j=0 c jZ n-j, n ≥ 1} exists. A point process based on {X n } converges weakly and from this, a host of weak limit results for functionals of {X n } ensue. We study sums, extremes, excedences and first passages as well as behavior of sample covariance functions.