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...

We obtain limit theorems for a class of nonlinear discrete-time processes X(n) called the kth order Volterra processes of order k. These are moving average kth order polynomial forms: X(n)=∑0i1,…,ik∞a(i1,…,ik)ϵn−i1…ϵn−ik, where {ϵi} is i.i.d. with Eϵi=0, Eϵi2=1, where a(⋅)...

Many econometric quantities such as long-term risk can be modeled by Pareto-like distributions and may also display long-range dependence. If Pareto is replaced by Gaussian, then one can consider fractional Brownian motion whose increments, called fractional Gaussian noise, exhibit long-range...

Consider the sum Z=∑n=1∞λn(ηn−Eηn), where ηn are independent gamma random variables with shape parameters rn0, and the λn’s are predetermined weights. We study the asymptotic behavior of the tail ∑n=M∞λn(ηn−Eηn), which is asymptotically normal under certain conditions. We...

We introduce a broad class of self-similar processes {Z(t),t≥0} called generalized Hermite processes. They have stationary increments, are defined on a Wiener chaos with Hurst index H∈(1/2,1), and include Hermite processes as a special case. They are defined through a homogeneous kernel g,...