Open AccessA Beveridge–Nelson filters for the self normalization
Author(s) -
Mindaugas Juodis
Publication year - 2021
Publication title -
lietuvos matematikos rinkinys
Language(s) - English
Resource type - Journals
eISSN - 2335-898X
pISSN - 0132-2818
DOI - 10.15388/lmr.2007.24255
Subject(s) - normalization (sociology) , mathematics , infinity , zero (linguistics) , central limit theorem , combinatorics , class (philosophy) , limit (mathematics) , block (permutation group theory) , pure mathematics , mathematical analysis , statistics , computer science , philosophy , sociology , linguistics , artificial intelligence , anthropology
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.