  This paper addresses the following classical question: giving a sequence of
identically distributed random variables in the domain of attraction of a
normal law, does the associated linear process satisfy the central limit
theorem? We study the question for several classes of dependent random
variables. For independent and identically distributed random variables we show
that the central limit theorem for the linear process is equivalent to the fact
that the variables are in the domain of attraction of a normal law, answering
in this way an open problem in the literature. The study is also motivated by
models arising in economic applications where often the innovations have
infinite variance, coefficients are not absolutely summable, and the
innovations are dependent.
