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

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