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Noncentral limit theorems for bounded functions of linear processes without finite mean | ||
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We derive noncentral limit theorems for the partial sum processes of K(Xi)]E{K(Xi)}, where K(x) is a bounded function and {Xi} is a linear process. We assume the innovations of {Xi} are independent and identically distributed and that the distribution of the innovations is an Ώ-stable law (0<Ώ<1) or belongs to the domain of attraction of an Ώ-stable law (0<Ώ<1). Then we establish the finite-dimensional convergence in distribution of the partial sum processes to an Ώΐ-stable Levy motion. The parameter ΐ determines how fast the coefficients of the linear process decay and we assume that 1<Ώΐ<2. We also derive the asymptotic distribution of the kernel density estimator of the marginal density function of {Xi} by exploiting one of the noncentral limit theorems. | ||