A central limit theorem for self-normalized sums of a linear process

Let Xt=∑i=0∞ψiεt-i be a linear process, where ∑i=0∞i|ψi|<∞ and ɛtɛt, t∈Z,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. We prove a central limit theorem for self-normalized sums Un-1∑t=1nXt, where Un2 is a sum of squares of block-sums of size m, as m   and the number of blocks N=n/mN=n/m tend to infinity.