A Beveridge–Nelson filters for the self normalization

Let Xt =Σ∞i=0 ψi εt−i be a linear process, where εt , 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−1n Σnt=1 Xt , where U2n is a sum of squares of block-sums of size m, as m and the number of blocks N = n/m tend to infinity.