A strictly stationary, "causal," 5-tuplewise independent counterexample to the central limit theorem
Probability
2009-11-17 v1
Abstract
A strictly stationary sequence of random variables is constructed with the following properties: (i) the random variables take the values -1 and +1 with probability 1/2 each, (ii) every five of the random variables are independent, (iii) the sequence is "causal" in a certain sense, (iv) the sequence has a trivial double tail sigma-field, and (v) regardless of the normalization used, the partial sums do not converge to a (nondegenerate) normal law. The example has some features in common with a recent construction (for an arbitrary fixed positive integer N), by Alexander Pruss and the author, of a strictly stationary N-tuplewise independent counterexample to the central limit theorem.
Keywords
Cite
@article{arxiv.0911.2905,
title = {A strictly stationary, "causal," 5-tuplewise independent counterexample to the central limit theorem},
author = {Richard C. Bradley},
journal= {arXiv preprint arXiv:0911.2905},
year = {2009}
}