The asymptotic behavior of quadratic forms in heavy-tailed strongly dependent random variables

Piotr S. Kokoszka and Murad S. Taqqu

Stochastic Processes and their Applications, 1997, vol. 66, issue 1, 21-40

Abstract: Suppose that Xt = [summation operator][infinity]j=0cjZt-j is a stationary linear sequence with regularly varying cj's and with innovations {Zj} that have infinite variance. Such a sequence can exhibit both high variability and strong dependence. The quadratic form 89 plays an important role in the estimation of the intensity of strong dependence. In contrast with the finite variance case, n-1/2(Qn - EQn) does not converge to a Gaussian distribution. We provide conditions on the cj's and on \gh for the quadratic form Qn, adequately normalized and randomly centered, to converge to a stable law of index [alpha], 1

Keywords: 60F05; 60E07 (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (3)

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