Central Limit Theorem for Linear Processes with Infinite Variance

Magda Peligrad () and Hailin Sang ()
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Magda Peligrad: University of Cincinnati
Hailin Sang: Indiana University

Journal of Theoretical Probability, 2013, vol. 26, issue 1, 222-239

Abstract: Abstract This paper addresses the following classical question: Given 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.

Keywords: Linear process; Central limit theorem; Martingale; Mixing; Infinite variance; 60F05; 60G10; 60G42 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10959-011-0393-0

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