Limit theory for moving averages of random variables with regularly varying tail probabilities
Let {Z_k,-∞<k<∞\} be iid where the Z k's have regularly varying tail probabilities. Under mild
conditions on a real sequence cj, j≥ 0 the stationary process X n:=∑∞ j= 0 c jZ nj, 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.
conditions on a real sequence cj, j≥ 0 the stationary process X n:=∑∞ j= 0 c jZ nj, 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.
Let 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: = ∑∞j=0 cjZn-j, 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.
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