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

Let \Zₖ, - < k < \ be iid where the Zₖ's have regularly varying tail probabilities. Under mild conditions on a real sequence \cⱼ, j 0\ the stationary process \Xₙ: = ^₉=₀ cⱼZ₍-₉, n 1\ exists. A point process based on \Xₙ\ converges weakly and from this, a host of weak limit results for functionals of \Xₙ\ ensue. We study sums, extremes, excedences and first passages as well as behavior of sample covariance functions.