A Beveridge–Nelson filters for the self normalization

Abstract

Let X_t =Σ^∞_i=0 ψ_i ε_t−i be a linear process, where ε_t , t ∈ Z, are i.i.d. r.v.’s in the domain of attraction of a normal law with zero mean and possibly infinite variance. Generalizing the class of Beveridge–Nelson filters this article proves a central limit theorem for the self-normalized sums U⁻¹_n Σⁿ_t=1 X_t , where U²_n is a sum of squares of block-sums of size m, as m and the number of blocks N = n/m tend to infinity.